I am sure that there will be differences of opinions. Here is my view.
The idea of the hunter being hunted is popular because it introduces a paradoxical sense of justice, which is satisfying.
In the beginning of the story, Rainsford is arrogant. When Whitney, his friend, suggests that animals might feel, Rainsford dismisses this as foolish. Rainsford has a crude classification system. Either one is a hunter or one is a huntee. Rainsford comes off as an insensitive man. When he meets Zaroff and becomes the object of the hunt, the tables are completely turned. This is somewhat gratifying. The text says that Rainsford now understood something: "Rainsford knew now how an animal at bay feels."
The tables are turned once again in the story, because Rainsford proves to be resourceful. He goes to Zaroff's house and waits for him. As he does this, he forces Zaroff to feel what it is like to be hunted. Again there is a feeling of satisfaction, because justice is introduced.