If the center of mass is ever so slightly off of the recoil's vector of force, the gun will pivot around it.

That translates to the muzzle rising as the gun does a fraction of a rotation around your shoulder in most firearm designs.

let's assume the chinese mobsters use the type83 smg, a modified chinese version of the PM63.
as you se int he immage, the upper reciever, bolt and all that other crap is situated above the trigger, so when you fire the gun the entire bolt will move backwards and forwards.
since it is situated above the trigger it will push your hand uppwards from that direction.
that is my theory off why the recoil would pull the gun sideways.

and no i am not saying all the chinese mobsters used this SMG, but the concept works on most regular SMG's

But yea, technically this would mean no matter how you held the gun it would climb vertically. Once again, I'm probably not right.

Recoil depends on the way you hold the gun and the way it interacts with your hand. If you hold it normally, it pushes your hand backwards. You hold handle of gun vertically, so it kind of jumps up because you can't hold still. If you move gun to horizontal position, the gun bumps into your hand and back horizontally also. It can't go up, because there's no force pushing it up, just sideways.

This is 100% true, I played a lot of Call of Duty so I'm verified gun expert.