[Ashmire]

Another diagnosed Aspie here...Beta and Shaidar have some good suggestions, but one thing I'd like to point out, a lot of people seem to focus on the idea of the phone/iPad *being* the distraction.  In fact, it's likely to be a coping mechanism, albeit one that can sometimes backfire( and other times, it actually does work, though it doesn't sound like it's doing that well for him, if you really do have to explain things to him. But I find people are most likely to accuse me of "not listening" when I am actually taking in the most information, and vice versa)
---but often, I find there is so much background noise around the table, completely unperceived by the NTs there, that I can't hear what the GM is saying anyway, and I know from experience being honest about this never works and usually causes even worse offense than having an obvious distraction ( which may at least let me be productive in another way).   In that case, a few more visual props and informational handouts can make a world of difference, if that won't be too disruptive to your gaming style, and I'd think could be fun even for NTs.  But then, that's assuming he does have the same kind of problems I do.  Clearly he hasn't got all the same issues since he seems to be noisy and I'm more prone to excessive silence/actual bouts of mutism.  Which is also undoubtedly annoying in a game where descriptiveness is valuable.

[Spooky]

Thank you to Shaidar and Ashmire. I now have a clue as to how to deal with non-NT issues. This is important because I teach classes at my LGS for both players (on how to play) and GMs ( how to run the game).

[TheWayfinder]

A player that is intentionally disruptive doesn't last long at my table.  I don't have time to mess with such a person.  I just tell him he's not invited to my table again.

Because I have rules for my table that every player knows beforehand, and this is for any RPG I play.  I've got them written down and everyone signs a sheet that says they've read and understood the rules. 

One of them is don't bring your books unless I, as GM, allow it.  Because it can clutter up the table.  I don't mind tablets and phones, but you don't use those to roll dice at my table; I don't allow using dice apps.  Not that I don't think they're good, it's mainly because I often can't see the results from where I usually stand.  I am tinkering with Fantasy Grounds, and may decide to use that system for my upcoming games. 

I generally allow my players to play their characters however they want.  If they want to be bloodthirsty and stupid, fine.  They suffer the consequences of this.  My other players would likely have killed your particular player's character if he got too far out of line, because they play as professionals, and the last thing they want is a loose cannon who could get them killed, or arrested, or worse. 

Usually, most players that behave badly have other issues at play.  As others have said, he might have Asperger's, but I often wonder if a lack of social graces is a product of our modern, smartphone/internet age, where we don't have to interact directly with one another.  Whatever it may be, I don't worry about it, because the rules are the rules.  I have people clamoring to get into my Shadowrun PDX game because I work real hard to keep it fresh, exciting, and consistent, so I don't have to care about kicking someone out if they're violating my rules.  (In fact, I'm thinking of charging tickets to play in my campaign.)

You may not have that luxury.  I fear, for your situation, that by being kind and adapting to that player, you may end up making a very dry game without much role-playing, rather like a standard D&D dungeon crawl that doesn't really concern itself with whatever characters the players may be playing.  And that may not be what your other players are wanting to play.  Individual players get something different out of a game, and you have to think about them too, and not let one player become a problem for the others to have to put up with and undermine their enjoyment of the game you're running. 

Out of full disclosure, I don't know fully what the situation is beyond what you described, so maybe my suggestions might not be very good for you. 

[The Wyrm Ouroboros]

This sounds like it may have progressed well beyond the 'talk to the guy' stage - that it's been tried, and repeatedly.  The following advice assumes that this is so.  That having been said:

For His Fellow Players
If the Troublesome Player (hereafter TP) isn't physically there (keeps going to the bathroom, getting up and leaving the room, whatever), tell him he's 'in the back', and if he wants to know what's going on, he'd best pipe down and pay attention - to listen carefully to what IS going on right at that moment, so as to figure it out for himself.  To be blunt, stop leading him around by the nose; learn how to turn fifteen minutes of the rest of the group's RP into 'we're off to kill this guy', or whatever the current plan is - and keep it very bare-bones.

If there's an actual plan, again, bare-bones it: tell him the ops that y'all decided for him.  If TP bitches or disagrees, then look him right in the eye and reply with absolute calmness, "Well, you should have been around when we were planning."  Then go ahead with the plan.  And if he deliberately screws up your plan, act like shadowrunners: lock up his gear and 'ware, then put two into the back of the character's skull and leave him behind.

For The GM
Simply, actions have consequences.  Warn him first - but at this point, warn him only once.  I and my various groups have had significant success with the simple rule of "Enough is enough; unless you specifically say so beforehand, your speech and actions and lack thereof at the table are your character's speech and actions in the game world.  If you want to participate, to have a say in the matter, to know what's going on, then you need to be at the table both physically and mentally.  If you just want to be casual and hang out, then actually having a character in the game isn't the right thing for you; maybe you could play Diablo III over there while we're playing SR5 over here."

If he sticks with the game, then inform him straight out that he's progressed past the 'talk to him' stage, and now it's time to get into the penalty phase.  Tell him that "You weren't here.  They left without you." will be a perfectly valid resonse, and one that may lead to desperate interaction on his part as he tries to hook back up with the group.  Or "You weren't paying attention, so it sounds like you didn't get paid."  Or "Apparently your character was playing LokBlokx on his commlink and tripped the alarm / got shot / whatever stupid thing you walked into because you weren't here to direct your character's actions."

In short, he's a strain on the group, both in and out of character.  It's time to inform him that he can either fish, cut bait, or ease on out of the boat.  You like hanging with him, but either he's there to play the game (IMO, doubtful), or he's there to hang out, and if it's the latter, then hey - hang out but not be part of the game.  And everyone will be happier.

[Dampfish]

OP here:
I don't know how/why the conversation became one about non-neurotypical diagnoses etc, but I suppose that could be of help to someone in the future.

As for my own problem, I'm actually happy to report that it has been worked out. The player in question quit of his own accord the last time we played. We sat down with him and I was prepared to work something out diplomatically, but apparently just being "formally" told off was too much for him and he quit the group altogether...
His choice, though I can't say that I'm complaining. (That might sound harsh, but I'm having to deal with bipolar myself. GM-ing is partly a sort of self-treatment for me and his shenanigans did not help.)
Hence why I have been mostly ignoring this thread since.

Anyway, that's my piece.
Tthe tips on handling non-neurotypical players were pretty interesting and will probably be useful - so as you were

[Shadowjack]

I see these kinds of threads all the time across the net, from system to system. You just need to put your foot down, if you don't he is going to screw the game up for you. First of all, there should be no phone usage at the table whatsoever. If someone isn't paying attention they are not worthing having at the table.  Sometimes you need to kick people and risk losing a portion of the group. A small group of people paying attention and learning the rules is better than a larger group with a single person ruining the fun for the GM. If he's not going to bother to learn the rules and put his phone away, tell him goodbye.

*Edit* Just saw your last post but I'll leave this here in case someone else happens upon it.

[AwesomenessDog]

What is the guys job, especially relative to the other girl who works with him? This may sound stereotypical but its at least as likely that the guy has autism (Aspergers is not really a thing, read the DSM 5 researcher's notes before you shoot the messenger), but he might just be a boss of her or someone else in the company and has gotten used to having info spoon fed to him and is turning to his phone when he isn't getting whats immediately relevant to him.

Rule number 1 with electronics is that when its not being passed to the gm, it should be flat on the table face up so everyone knows its relevant, not metagame related, and not a distraction. Rule two amends that when someone is separated from the IC group, it is customary to allow earbuds turned to medium volume and be listening to music to prevent metagaming. Anything else and it's taking away from the game.

It sounded like he didn't have the books which I personally wouldn't blame him for not understanding most of it since he can't study it but I also say that the gm isn't doing his job if the players have to know anything besides Ability+Skill [Limit] math; rules are doorways, not walls.

If you are worried about people thinking you're a dick gm because you want to get rid of a player, speak to them individually (because in a group makes it seem like your conspiring against him instead of trying to handle an issue) about how they view the person and if they "want to keep him" instead of "how would you feel if I kicked him out".

Too late now but there is always a next time, if he asks "what is going around me again" just tell him he wasn't paying attention in character and see if the players will tell him. Neurotic or not, if he can't equate real attention to IC attention, then you have bigger fish to fry. Depending on his character archetype, it could be really easy to punish him into awareness: if he is the decker or AR rigger, say a grenade landed next to him and he didn't notice and his hand is now gone; if he's a mage, well you know what to do...

The worst case of this I ever encountered was someone who (I wasn't gm) brought his laptop to every game when he already had a paper character sheet and played music throughout the entire game. He was a douchy person so he knew he was fucking with us, not someone with mental issues. Let's just say sometimes you have to make it personal to get them to stop.

[Shaidar]

[...] (Aspergers is not really a thing, read the DSM 5 researcher's notes before you shoot the messenger) [...]

It used to be, ASD has only been the "proper" term for the last 3-4 years. Many of us former Aspies who would now be diagnosed with ASD have lived with, and prefer to be identified by, the term Asperger's which was taken from the first psychiatrist to identify the syndrome back in 1944. So I at least wasn't using Asperger's as a medical term but more a social/societal identifier.

[AwesomenessDog]

[...] (Aspergers is not really a thing, read the DSM 5 researcher's notes before you shoot the messenger) [...]

It used to be, ASD has only been the "proper" term for the last 3-4 years. Many of us former Aspies who would now be diagnosed with ASD have lived with, and prefer to be identified by, the term Asperger's which was taken from the first psychiatrist to identify the syndrome back in 1944. So I at least wasn't using Asperger's as a medical term but more a social/societal identifier.

In that case, I would point out that many have found Asperger's research to be fraudulent and only existed because the man wanted to save his patient's lives from the Third Reich. If the Nazi medical community determined that Asperger's patients were no longer necessary, they would be executed, so Asperger made the moral decision at the cost of his research being not credible. However since the person in question would not have been diagnosed or simply a latent developer, it would be wise to refer to what medicine knows now and not what we thought we knew.