At the start of the short story, Whitney and Rainsford discuss the feelings of the jaguar being hunted, and Rainsford points out that "[t]he world is made up of two classes—the hunters and the huntees." The defining characteristic that Zaroff and Rainsford share is that of being in the same class: the hunters.
After Rainsford falls overboard, he swims towards the sound of gunshots and screams of pain and fear. When Rainsford wakes up on the island, he encounters the patch of underbrush where the screaming creature must have died. He uses the same skills of observation honed by his hunting experience to come to this conclusion, the same skills that Zaroff, another experienced hunter, must have used to pursue and kill his prey.
When Zaroff and Rainsford meet, after Rainsford has confronted Ivan at the door of Zaroff's mansion, Zaroff starts his hunt with clever and witty intimidation tactics. These tactics are typical results of a hunter's "analytical mind," which Rainsford also possesses, as a hunter. Zaroff claims prior knowledge of Rainsford and admits to Rainsford that he is like Ivan, a "savage," in an attempt to disorient Rainsford and place him in a position of weakness. The appraising looks from Zaroff that bother Rainsford during dinner are also tactical, to put Rainsford on the defensive.
When Zaroff concedes that Rainsford has won the game at the end of the story, Rainsford insists that the hunt continue and that the two hunters fight to the death: "Get ready, General Zaroff." Rainsford's hunting instincts lead him to mistrust Zaroff, and he kills Zaroff knowing that that is the only way he will live. To the end, neither hunter can turn off their hunting skills, perhaps the mark of a true and lifelong hunter.