Just as there exists an irony throughout the narrative of Richard Connell's story when Rainsford disdains Whitney's concern for the jaguar as prey but later understands being a "beast of prey," and when Rainsford tells Zaroff after hearing of the general's "game" that he does not "condone cold-blooded murder," but later himself commits such an act, there is an irony to the title.
Two interpretations of this title are that, on the one hand, General Zaroff, in his jaded state of ennui with the customary hunts of wild game, has created a situation on his island where he can hunt the most challenging game: man. He has created a dangerous game, or hunting sport. On the other hand, this dangerous game that he has created becomes, ironically, for Zaroff the most dangerous prey, or "game" as the animal of pursuit, he has ever encountered. For, the prey, Rainsford, as a "beast at bay" turns predator and kills the general. Thus, the irony of the title becomes apparent: the game has changed from a sporting contest in which Zaroff is the hunter to Rainsford's becoming himself the hunter who deals a deadly and fateful end to the former predator.
In order to understand the two meanings, one can place the emphasis on the word Game implying that man in general is the most dangerous of game animals, or one can place the emphasis on The implying that Rainsford himself becomes the most formidable of the dangerous prey, man, that Zaroff has ever hunted. (The Most Dangerous Game vs. The Most Dangerous Game)
The two meanings of this title depend on the two meanings of the word "game" in modern English. The word "game" can mean either a contest (as in a game of football or a game of chance) or it can mean prey (as in a game bird or a game preserve).
In this story, both meanings apply. A human being is the most dangerous prey to hunt (potentially) because, as Rainsford does, it can use its intelligence and its hands to devise ways to trap the hunter. Because it is so dangerous to hunt a human, doing so is the most dangerous contest, or game.