Thinking about this...Have you seen that very early Tyson video, where he is working with Cus, and moving his head side to side and jabbing to Cus's palm? This is where you get screwed up with 'side-to-side' stuff in boxing...
In the videos posted, Tyson makes that move to the side and jabs, but he doesn't close distance and his feet aren't in a position to throw another punch. If you make that move correctly- you slip it by rolling towards the punch- that all changes.
You slide the left foot forward, roll your right shoulder like if you were throwing a right hand, and jab. You've closed distance, you are throwing a very stiff straight left hand (because your weight is going from the left foot back to the right), and you are in a position to throw a right hand, or to duck/bob/weave/etc... to avoid a possible counter.
Tyson left himself, in each clip, standing on one foot, all his weight in one place. If the opponent had punched back, he had to get hit. You can't do much with all your weight on your left leg.