As he proves himself at the end of "The Most Dangerous Game," Rainsford is a true predator--"I am still a beast at bay" he tells Zaroff. Then, the last line of the narrative confirms his enjoyment of his having finished off General Zaroff: "He had never slept in a better bed, Rainsford decided."
The "most dangerous game" has taught Rainsford much about himself. In the exposition he does not concern himself with whether a jaquar feels pain, telling Whitney who poses this thought, "Bah! They've no understanding." What predator does care about the feelings of his prey? Rainsford continues, "Be a realist. The world is made up of two classes--the hunters and the huntees." Clearly, at the story's end, Rainsford expresses his pleasure at being the hunter. He decides this is what he is.
Unlike Zaroff, Rainsford takes no pleasure in the idea of making others fear or suffer. The very thought of a jaguar actually being in a panic while it is being hunted is an unpleasant thought. Through denial and compartmentalization (two defense mechanisms), Rainford convieniently dismisses this otherwise evident fact - that is, until the tables turn and he finds himself in the role of the "huntee" instead of the "hunter."
The end of the story doesn't disclose whether Rainsford eventually had another attitude towards the animals he hunted or not. However, the possibility that he might have more "empathy" for an animal on the run is an interesting thought...