The point of view of "The Most Dangerous Game" is third person limited. Even though it seems that you find out a great deal of information about Zaroff, the story chronicles more of the adventures and feelings of Rainsford. One example of this is during the hunt; at this point in the story you only get a look at Rainsford's point of view. This is also true in the closing scene of the short story.
The narrator is not given a name, which is usually the case with most stories written in third person point of view.