The answer to this question leans heavily on the matter of characterization. In "The Most Dangerous Game," Rainsford is characterized as the good guy, and he engages in a man-to-man conflict with Zaroff, who is characterized as the bad guy. The tension between good and evil is heightened when the conflict becomes a fight to the death between the two men.
Even at the start of the short story, Rainsford is characterized as resourceful and capable. For example, he relies only on himself when he goes overboard: "A certain coolheadedness had come to him; it was not the first time he had been in a tight place." When he lands on shore, he sleeps deeply, despite hearing eerie screams and the sound of gunshot; when he wakes up, he looks around "cheerfully." This resilience is the mark of a hero.
Zaroff is characterized through Rainsford when the reader first meets him. Among other physical characteristics, Zaroff "had high cheekbones, a sharpcut nose, a spare, dark face—the face of a man used to giving orders, the face of an aristocrat." From the start, Rainsford's impressions indicate to the reader that Zaroff is not like "us," which is one way to characterize a villain, and Zaroff looks like he prefers to be in charge, unlike the likable hero of Rainsford.
So, in this story, the man versus man conflict here is enhanced by tension between the hero and the villain, Richard Connell's representatives of good and evil.