[Tirwalker]

Do the martial arts styles and maneuvers from Run and Gun count as positive qualities (total positive qualities of 25 points) or do they fall in their own category, like extra skills, attributes, and nuyen?

[Sabato Kuroi]

They are not qualities as far as I know

[Imveros]

they are not qualities they are simply add ons.

Run and Gun page 128

Each martial art style has six techniques for a character
to choose (listed under Available Techniques).
Buying a new style costs 7 Karma, and when you buy
that style you may then choose a technique to go with
it. Buying additional techniques costs 5 Karma. At character
creation, you can buy up to 5 total techniques, in
a single style, which costs 27 Karma. You can only buy
one style at character creation.

if they were positive qualities you couldn't buy 4 additional techniques like is listed here. They also aren't listed in the positive qualities section like One trick pony is

RG p127

ONE TRICK PONY (–7 KARMA)
You’ve watched the same action trid or chipped your
way through the same simsense so many times you actually
know how to do that really cool move the star
always uses. This quality allows the character to choose
one Martial Arts technique they can do without first
learning the associated Martial Arts style.

[k_night]

yeah i dont get one trick pony
for the same price you get an actual MA and technique
and it doesnt count towards your PQ limit
and if you ever decide to get another technique you dont have to pay the full price

[Michael Chandra]

One Trick Pony has 2 advantages.

1: It lets you get a technique from a second Martial Arts if you already learned 1 MA in chargen.
2: It lets you learn techniques that are not covered by any Martial Arts.

The second is real important. For example, some techniques exist in different weapon flavours but not all of those are covered by Martial Arts.