What is "the punishment game?" From what I've taken so far, it's the moment after the moment you say
"Oh crap I shouldn't have done that?"
The short version is this (yeah right, "short"):
Every move that you do takes a certain amount of "frames" to execute. One frame is a 60th of a second, AKA there are 60 frames in a second. In addition to this, moves also take frames to recover before you can do anything else. These are called positive (length time of move start-up) and negative (how long until your character recovers from performing the move) frames. Attacks are "safer" if they have low positive and negative frames.
Now, the two general ways you would punish would be if you blocked an opponent's attack, or if the opponent whiffs (misses completely and makes no contact.) This means they would be open for attack, because the moves they just executed would have negative frames that they have to wait out before they can do anything else like guard. You retaliate by following up with a move that has LESS positive frames than their last moves' negative frames. Otherwise, you'd be too slow and you lose your punishment opportunity.
Different moves have different frame timings. The idea is to know which moves you have that would be fast enough to punish the other guy's attack.
An example:
Your opponent hits you with a move that is -10 frames on block. This means that if you block, you can respond by attacking with a move that takes less than 10 frames to execute and it will hit him.
Inversely, you can also punish people for trying really slow moves, AKA moves with a lot of positive frames. If you interrupt, say, a move that is 30 frames long with a 10 frame move, you will have been faster than him, therefore you hit him before he even touches you. This is how Counter Hits happen, and you'll get extra little rewards in gameplay from that in various ways.
Hope I explained it semi-well. And I hope you weren't confused by the game-theory... Frames are an important concept to learn in fighters.
