The climax of Richard Connell's short story, "The Most Dangerous Game," comes when Sanger Rainsford manages to elude the murderous Russian Cossack, General Zaroff, diving off a cliff into the waters below in his last-ditch effort to escape his hunter. Rainsford had managed to elude Zaroff for more than a day, killing Zaroff's companion, Ivan, and one of the dogs; Zaroff, too, had been injured. But Rainsford realized his time was running out and, when reaching the cliff, he decided to take his chance with the dangerous dive rather than with Zaroff's relentless pursuit. The latter paragraphs of the story, when Rainsford returns to Zaroff's bedroom, serves as more of a falling action after the exciting hunt.
I would say the climlax is the scene on the cliff when Rainsford is faced with a life or death situation and decides to throw himself from the cliff rather than face the man who has been hunting him, General Zaroff.