The two meanings of “game” in the title are “play” and “hunted animal.”
The word “game” is used to refer to animals that are hunted. For example, tigers, rhinoceroses, and bears are all game. Rainsford is a big-game hunter and an author of books on hunting. As expert as he is, he finds that Zaroff has something else in mind.
The Cape buffalo is not the most dangerous big game." He sipped his wine. "Here in my preserve on this island," he said in the same slow tone, "I hunt more dangerous game."
The game that Zaroff hunts is human beings. They are the most dangerous of all game because they can reason. An animal that can think has the potential to outsmart you or at least make the hunt more interesting. This is why Zaroff has been capturing and hunting sailors and other dregs of society that will not be missed.
Part of the fun of the title is in the word play. The double meaning of “game” is a wink at the reader. A game, of course, is played between people. Usually there are rules in a game that must be followed, and there is always a winner or a loser. In Zaroff’s game, the loser dies.
"It's a game, you see," … If my quarry eludes me for three whole days, he wins the game. If I find him "--the general smiled--" he loses."
We know that Zaroff is enjoying the game because he toys with Rainsford, turning back to give him another day and make him feel more terror. To make things even more interesting, Rainsford is a skilled hunter and wants to live more than anything. He wins the game by outsmarting Zaroff and getting into his room. Then he changes the rules by killing Zaroff, therefore really winning the game.
The surprise ending catches the reader even more unaware. We might have wanted Rainsford to win, and Zaroff to lose, but we didn’t expect Rainsford to kill Zaroff. It brings another moral quandary to the story. Was he justified? If he hadn’t killed the general, would the general have kept his word and played by the rules of the game, or would he have cheated and killed Rainsford anyway? After all, he couldn’t let Rainsford go. He would tell someone, and that would be the end of the game—in every sense of the word.