"The Most Dangerous Game" is told from the omniscient third-person point of view, as bullgatortail states above. The story could not be told from the first-person point of view of either Rainsford or Zaroff because of the principle stated by Vladimir Nabokov: "The I in the story cannot die in the story." The first-person narrator must be alive to tell how the story ends. (An author could experiment by telling a story in which the first-person narrator actually does die but becomes a ghost and continues telling the story from his point of view.) If the author Richard Connell had written his story from the first-person point of view of Rainsford, we would know that he had not really been in mortal danger, since he would still be alive to tell the story at the end. And if Connell had tried to tell it from the first-person point of view of Zaroff, which could be intriguing, we would naturally assume that the general was going to win the "game" of death. But by having an invisible, omniscient narrator telling the story, the reader can be kept guessing about the final outcome. Another possibility would be to keep switching points of view from Rainsford's to Zaroff's. In that case, the story might end from a third point of view, that of Whitney for example, who arrives on the island and finds both men dead.
Richard Connell chooses to use an omniscient third-person narrator for the telling of his short story "The Most Dangerous Game." Connell uses the narrator to tell much of the story from Rainsford's point of view. However, after Rainsford escapes Zaroff near the end of the story, Connell shifts for a short time to Zaroff's perspective as he returns from the hunt to enjoy a last meal. Some critics believe Connell's reasoning for the change is to show that Zaroff--the hunter throughout the story--has now become the hunted. In the final sentence, the focus shifts back to Rainsford's view as he decides that
He had never slept in a better bed.