Rainsford is the protagonist of the story, and serves the role of both hero and underdog; he is the person intended to receive sympathy from the reader, and he is vastly outgunned by General Zaroff. As a character, he is simply drawn; the story has a "cold open," with no information about Rainsford beyond what can be gleaned from the conversation. When he meets Zaroff, it is revealed that Rainsford is not only a very famous big-game hunter, but the author of a popular book on hunting.
Desperately he struck out with strong strokes after the receding lights of the yacht, but he stopped before he had swum fifty feet. A certain coolheadedness had come to him; it was not the first time he had been in a tight place.
(Connell, "The Most Dangerous Game," classicshorts.com)
Rainsford is determined and self-sufficient; even when thrown from his boat in the middle of the ocean in pitch-black night. His determination serves him well later, as he refuses to give up, even when all his traps fail to kill Zaroff. He seems to be a moral person, holding human life higher than animal life, but is also willing to kill to preserve his own life. In essence, he is the polar opposite of General Zaroff, who kills humans for pleasure; Rainsford has a personal moral code, which he is forced to break for his own survival.
It is hard to take "The Most Dangerous Game" terribly seriously. General Zaroff is a stereotypical adventure-story villain, and Rainsford is a stereotypical adventure-story hero, the kind of man that boys admire and would like to be. Rainsford is a man of action, strong, silent, handsome, athletic, poised, sophisticated, unflappable. The line that seems to characterize him best is: "...it was not the first time he had been in a tight place." He could hardly find himself in any tighter place than he is in "The Most Dangerous Game." He has to swim through an ocean infested with man-eating sharks in order to get to an island where the owner hunts humans for sport. This is about as fantastical as Jurassic Park, where the eccentric scientist, who has money to burn, is raising dinosaurs to stock an amusement park. Rainsford may or may not be an American citizen, but he seems patterned after the older British strong-silent heroes of authors like H. Ryder Haggard, or like James Bond as played by Sean Connery. I don't think we ever feel that he is ever in real danger or that he won't come out on top.