some of the folks complaining here don't seem to have had any H2H or CQB training.
The technique he uses in the movie is actually a Krav Maga disarm.
You will notice that he is not lightning-quick, but the key to his engagement is the disarm. He grabs the BG1's handgun, deflects the muzzle away from him, and towards the general vicinity of BG1, and possibly BG2 (hard to tell from the angle).
He is quick when he does this, but not so quick that it's Holywood fake.
All this is done at a 1.5 rhythm, where the deflection takes place first, then while maintaining the disarm, drawing your sidearm and engaging.
It's really a cool technique, and I especially like how he shoots the first dude from the guard position, then finishes the other guy with a full extension.
I am taking a class on this stuff next month. Can't wait.