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.