Adventures, for example, whether text or graphic, are puzzles. Tetris and its clones are puzzles. They are differentiated by the ability of the opponents to impede each other's performance. If the opponents are constrained from impeding each other and instead devote the bulk of their attentions to maximizing their own performance, then the conflict is a competition. If on the other hand, they are permitted to hurt each other's performance, then the conflict is a game.
Examples are races and political campaigns.
This leaves games as conflicts in which the players directly interact in such a way as to foil each other's goals. In other words, if you can shoot back at the other guy, and he shoots at you in a manner that convinces you that he's out to get you, then it's a game.