A degenerate game has very little strategic depth. Tic tac toe is a good example.
Degenerate games can be played using very simple strategies with no meaningful decision making. These are known as degenerate strategies. A good game design does not allow degenerate strategies.
Usage: I wish we could include an exploding squirrel character, but it would open up a whole slew of obvious degenerate strategies.
Comment: Degenerate strategies can be fun to add here and there, but only as a temporary exception to the rule. If players have been fighting monster X hard for the whole game, they might enjoy a few minutes with an exploding squirrel gun that kills him in one hit. The game wouldn’t work if he had that gun the whole time, though. A real example of this is the invincibility star in the original Mario games.