Rainsford is a skilled hunter in excellent physical condition with an analytical mind. He is a World War I veteran, who
... had dug himself in in France when a second's delay meant death.
So, the hardships of physical exertion and endurance is not new to him. He has already displayed his physical skills by surviving the fall from his yacht and making the treacherous swim to the shore of Ship-Trap Island. When Zaroff forces Rainsford to become the prey of his next special hunt, Rainsford sets out at a fast pace, hoping to distance himself from his pursuer. He survives two nights on the run and still has the strength to make his final swim from the cliffs back to Zaroff's chateau.
Although Rainsford feels "panic" at the beginning of the hunt, and he later comes to understand "the full meaning of terror," he constantly reminds himself that
"I must keep my nerve. I must keep my nerve."
... had got a grip on himself, had stopped, and was taking stock of himself and the situation. He saw that straight flight was futile; inevitably it would bring him face to face with the sea. He was in a picture with a frame of water, and his operations, clearly, must take place within that frame.
He recognized that he was Zaroff's prey in this deadly game, but Rainsford resorted to several tricks he had learned from his journeys to Africa and Asia--tricks used by hunters of a different kind. Although his flight seemed "a desperate, hopeless" one, his cunning traps first injured Zaroff, and then disposed of Ivan and one of the dogs. At last, when he was presented with the option of certain death at the hands of Zaroff and the dogs, and the possibility of surviving the leap from the cliff into the waters below, Rainsford was clear-headed enough to make the logical decision. His final move--to double back and confront Zaroff in his own home--was a stroke of genius, and one that caught the unexpected Zaroff completely by surprised.