Instinct is an innate reaction, and something we do without thinking. One instinct humans have is for survival. When offered the choice of Ivan or the game, Rainsford chooses the game. He also plays the game, because his instincts tell him not to give in.
Sometimes a person has to fight his instincts. Rainsford’s instinct is to run, of course.
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.
Thought is also important. Rainsford uses his intelligence and intellect to win the game. When he falls off the boat, he swims toward the island and uses his experience to make inferences about what is happening.
Even so zealous a hunter as General Zaroff could not trace him there, he told himself; only the devil himself could follow that complicated trail through the jungle after dark. But perhaps the general was a devil--
Rainsford also realizes that the general really is playing a game with him.
Rainsford did not want to believe what his reason told him was true, but the truth was as evident as the sun that had by now pushed through the morning mists. The general was playing with him! The general was saving him for another day's sport! The Cossack was the cat; he was the mouse. Then it was that Rainsford knew the full meaning of terror.
With this realization, Rasinford works even harder to outsmart the general. He uses his knowledge of trapping and hunting, but the general is also knowledgeable. He has to use his intellect to win.
A man, who had been hiding in the curtains of the bed, was standing there.
"Rainsford!" screamed the general. "How in God's name did you get here?"
"Swam," said Rainsford. "I found it quicker than walking through the jungle."
In the end, Rainsford wins by outsmarting Zaroff.