Rainsford is, by definition, the protagonist in this story. As the main character and conceptual "good guy," Rainsford fills the role of protagonist well. The antagonist, in contrast, would be General Zaroff, as he is considered to be the adversary or "bad guy" in the context of the short story.
One can typically identify a protagonist by examining the character's actions, description, and the tone the author uses when writing about him/her. If the above criteria all point toward a character being the main, positive focus of the story, chances are, that character is your protagonist, just as Rainsford is.
The protagonist in a work of literature is the main character. In Richard Connell's "The Most Dangerous Game," the protagonist is the big game hunter Sanger Rainsford, who falls off his yacht and winds up on the island of General Zaroff. Rainsford had been on his way to South America to hunt jaguars with his friend Whitney. He is able to swim ashore to the remote island, which is uninhabited except for the chateau of Zaroff, a former Russian military man who has come to the island to indulge in his love of hunting. Unfortunately, Zaroff is a sociopath and he hunts men instead of animals. Because he ends up hunting Rainsford, he becomes the antagonist of the story. An antagonist is a character in conflict with the protagonist.
Oftentimes, the protagonist is considered a dynamic character because he changes over the course of the story. In this case, Rainsford is dynamic because his attitude over hunting is forever altered after his encounter with Zaroff. In the beginning of the story, Rainsford denies Whitney's assertion that the animals they hunt have feelings. Rainsford argues that animals have no understanding of fear or pain and are simply to be killed for the hunter's pleasure. This point of view changes during the "game" between Zaroff and Rainsford as the general tracks Rainsford through the jungle. Rainsford comes to realize and understand the terror of a creature being pursued. At the end of the story, he tells Zaroff that he is a "beast at bay" and winds up killing the general. While never revealed, the reader must assume that Rainsford will probably never hunt again.