The answer is: third-person point of view.
In the excerpt from "The Most Dangerous Game," the author Richard Connell refers to Rainsford as "he," "his" and "him." Even though he quotes Rainsford's thoughts, he uses the third person point of view to provide readers a more objective and broader perspective of the story -as outsiders- and the observation of Rainsford and other characters's feelings and ideas as well.