[Sleeptime]

p.294, Engulf:

Engulfed victims may not move. During the victim’s Action Phase, the victim may attempt to escape.

Beyond this, there's no indication the victim can't do other things, like speak, drop a grenade, or make a full fledged attack (melee or ranged).
I read it as "walking" move, not "any sort of twitch" move. Because if you can muster up the strength to break free entirely from an engulf, surely you can go through the tinier effort to pull a trigger which your finger is already on - which, in the case of the actual spirit engulfing you, would mean you will make an attack on it from the inside so that it can't dodge.

Please tell me I'm understanding this entirely wrong and it's the unanimous perception of the SR community that engulf actually does prevent you from doing anything else, thus making it not useless.

[Muscular_Bevar]

I'd rule that they can't do anything else apart from attempting to escape. (RAI?)

[Sleeptime]

I'd like to rule that too, but given that I'm not well versed in the balance of the system (lol) I don't know if I'm breaking it this way or the other way.

[Machiavelli]

Due to the fact that it is not mentioned that you cannot do anything else, i would allow an attack/dropping/whatever. On the other hand you have to use your common sense and ask yourself, IF you would do something else than trying to escape, while you are drowning/set on fire/crushed by earth/suffocated by wind/entangled by wines.....^^

[farothel]

And while you can pull a trigger, you can't move to bear the gun on whoever you want to shoot.  So you will just shoot straight ahead and probably not hit much, if the bullets can move outside of the engulf effect.