What is the climax of the story "The Most Dangerous Game"?

The climax in the plot of a short story is the highest point of interest. In other words, the reader should be at a point in the story where suspense has built up to an inevitable crisis. In Richard Connell's short story the climax is when Rainsford decides to jump into the ocean in order to avoid General Zaroff, who will most certainly kill Rainsford if he catches him. After trying every hunting trick he knows, including the Malay man-catcher and Burmese tiger pit, Rainsford finds himself on the edge of a cliff across from Zaroff's chateau. The general is being led by his pack of dogs toward Rainsford when the American leaps:

Twenty feet below him the sea rumbled and hissed. Rainsford hesitated. He heard the hounds. The he leaped far out into the sea....

Connell uses an ellipsis here to indicate that it is unknown whether Rainsford survives the jump or not. The falling action, which follows the climax, involves Zaroff going back to his chateau, dining and reading. When he goes to bed he discovers Rainsford, who has survived the swim (foreshadowed earlier in the story when Rainsford falls off his yacht and swims to the island), in his bedroom. They fight and, in the resolution of the conflict between the two men, Rainsford kills the general and sleeps in his bed.
Some might argue that the climax actually occurs when Rainsford reappears in Zaroff's bedroom; though there's a case to be made for this interpretation, the fact that the fight itself isn't described in detail leaves the scene reading more like traditional falling action. The reader's anticipation is greatest in the scene where Rainsford jumps off the cliff; thus I would argue that this scene, not the one in which Rainsford reappears, is better identified as the climax.

The climax of any story is the high point of the story.  The moments leading up to the climax are all part of the rising action, and anything after the climax is falling action and resolution.  The climax of "The Most Dangerous Game" is when Rainsford kills Ivan and escapes from Zaroff by jumping off the cliff.  This is by far the most tense and suspenseful part of the story, and the moments after this are not nearly as heart pounding.  When Rainsford jumps, the story is at its peak in terms of momentum.  
After this climactic moment in the story, Rainsford makes his way back to Zaroff's house.  Once there, he waits for Zaroff to return.  The story concludes with Rainsford killing Zaroff and sleeping soundly in the man's bed.  I have seen some interpretations that support this final scene as the climax, but very little detail appears in the scene itself.  The author hints that a fight ensues, but no explanation is given.  

The general made one of his deepest bows. "I see," he said. "Splendid! One of us is to furnish a repast for the hounds. The other will sleep in this very excellent bed. On guard, Rainsford." . . .
He had never slept in a better bed, Rainsford decided.

As you can see, Zaroff readies himself for a fight, and the next thing the reader gets is the information that Raisford slept really well.  We have no idea how intense the fight was.  Compared the cliff jumping sequence, the bedroom confrontation is much less climactic.  I would categorize the bedroom confrontation as the story's falling action.