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.