Zaroff is not really the one who sets literal traps the way that Rainsford does. Zaroff gives Rainsford a "choice" that could be considered a trap. He tells him that he does not have to play the game and that he can choose to fall into the hands of Ivan who will torture him. This is an obvious choice for Rainsford because at least if he agrees to play he will have a chance at survival. While Rainsford is being "hunted" he finds that there is quicksand on the island which has served as a trap for men in the past, but Rainsford does not fall victim to it. He sets his own trap there and manages to take out one of Zaroff's best dogs. The other "trap" would be that Rainsford is forced to the edge of the island and has to decide to face Zaroff who is closing in or to jump, possibly to his death, into the sea.
Rainsford cannot escape the game. If he refuses to be hunted, he will be tortured by Ivan, Zaroff's servant. If he surrenders, he will either be malled by dogs or shot by Zaroff. He could commit suicide by falling in quicksand or drowning himself. Ultimately, he decides to fight for his life.
Rainsford sets traps for Zaloff. The first is the Maley man-catcher, a trap in which a positioned tree falls on the hunter, but Zaloff escapes with a shoulder wound. The second is the Burmese tiger pit, which actually does kill one of Zaloff's dogs. The third consists of Rainsford's knife flying on a vine backwards at his pursuers. This trap kills Ivan. In the end, Rainsford does win the "game," when he surprises Zaloff in his bedroom.