An alternative use, other than blustering bar room confrontations, is when someone already has you wrapped up, or basically has their arms on the outside of your arms.

I've relied on the two handed shove to break clinches and body locks, if they aren't absolutely locked in...

Also, to meet an attack....

This bar fight chest pushing stuff is basic fundamental self defense 101, a perinnial favorite with the "how to" crowd.

There are gazillions of techniques, but fundamentally, unless you are dead drunk dopey it shouldn't hurt you. So its a free shot that very clearly establishes you are defending yourself, so you f-ing defend yourself without hesitation. By pushing you, he has demonstrated his hesitation, are we on the same page yet? Don't matter what style, whatever, you beat it with superior heart and focus, because you are a trained Mother F-er, and he's an idiot.

Why worry about the attack, its benign unless delivered by a pro, or you get caught off guard and fall over something...