The climax of "The Most Dangerous Game" comes when Rainsford jumps into the ocean.
Zaroff has been chasing him for days. After Rainsford failure on the first day, Zaroff played "cat and mouse" with Rainsford, letting the prey remain free for a while. When Zaroff comes again for Rainsford, Rainsford begins to use his wits and his experience, killing off one of Zaroff's dogs and later Zaroff's assistant, Ivan.
Despite his successes, Rainsford becomes cornered in a section of the island. The dogs are coming for him and he has nowhere left to run. The tension of the story reaches its peak as Rainsford makes a decision about how to respond to this impossible situation.
In a fit of desperation, Rainsford looks to his only escape—jumping off the cliff into the sea which waits far below. He takes this chance.
After this moment in the story, we are presented with conclusion and resolution. Though Zaroff and Rainsford have their final confrontation in the house and Rainsford kills Zaroff, this final meeting occurs by way of falling action.
The tension of the story has already begun to dissipate. Others might argue that the concluding confrontation between the two men represents the climax of the story, bringing the central conflict to a close. However, the central conflict of the story - Rainsford's battle for survival - is decided when Rainsford jumps into the sea.