After General Zaroff's henchman, Ivan is killed by Rainsford's Ugandan knife trap, Rainsford—who is afraid that he will be attacked by Zaroff's hounds—runs to the edge of the cliff and throws himself into the sea.
Later that night, General Zaroff enjoys a dinner in his dining hall, bothered only by "two slight annoyances": the difficult nature of replacing Ivan and the fact that "the American hadn't played the game."
Zaroff believes that Rainsford has cheated his way out of playing the game by circumventing its rules. By throwing himself off the cliff—and presumably hurtling to his death—Rainsford had managed to prevent Zaroff from experiencing the "victory" of locating and killing him. No other participant has stopped the game via a suicide, and Zaroff has always managed to win.
In reality, Rainsford hasn't stopped playing at all; rather, he has hidden his strategy by faking his own death. The story ends with Rainsford (who had survived the plummet and swam around the island) surprising Zaroff in his bedroom. A duel ensues, and Rainsford wins the game.
Zaroff believes that Rainsford has "quit" the game rather than play it out to the death. Rainsford is on the run and finds that his only escape- rather than death- is to jump into the sea. Zaroff sees this action and believes that his one worthy adversary has quit the game and chosen death by the sea rather than playing the game. Little does Zaroff know that Rainsford has not quit the game he has tried a strategy that ensures his eventual victory.