There are differing opinions on whether the climax comes at the moment Rainsford jumps from the cliff or when he is discovered to be hiding in Zaroff's room, behind the curtain. I would consider the moment of highest tension (climax) to be the moment when Rainsford jumps. This means that the falling action would be the last scene of the story, taking place in General Zaroff's bed. It would include Rainsford showing himself and informing Zaroff that the he is "still a beast at bay." However, it is implied that there is some kind of fight, perhaps a swordfight: "On guard" is a phrase usually uttered before a duel. The loser did provide a meal, or "repast" for the hounds, but likely it was after the duel ended between the men...and which Rainsford won, since he is sleeping in the bed as the story ends. Re-read the ending of the story to fully form an opinion as to how the final moments played out.
The falling action, which comes right after the climax, would be after Rainsford leaps off a cliff and into the ocean, to what Zaroff believes is his death. The hunt had been escalating up to that point. Zaroff, disappointed, heads home, has dinner, and retires to his room for the night. Rainsford, all the while is hiding behind the curtains in his room waiting to surprise him with the fact that Rainsford indeed has beaten Zaroff. The men exchange words and Zaroff leaves the house the loser of his own game for the first time and goes out into the night where he falls victim to his own hounds.