The primary conflict inThe Most Dangerous Game, is Rainsford vs. Zaroff. Rainsford fights to survive, as Zaroff hunts him. Rainsford uses traps he's learned as a hunter himself to slowly gain the advantage and ultimately turn the tables on Zaroff.
There is also a secondary conflict between Rainsford and himself. His entire life, Rainsford has been the Hunter (i.e. the Predator), he sees the hunt as a matching of wits between him and his prey, that he almost always wins. Even if he loses (i.e. what he hunts gets away) he still lives. Zaroff forces Rainsford to experience being the hunted (i.e. the Prey). This gives Rainsford a whole new understanding of hunting.
Zaroff also exposes Rainsford to what Rainsford could become, if he becomes too proficient as a hunter. Zaroff took to hunting humans because animals didn't pose enough of a challenge anymore. There was no peril to Zaroff if he "lost," and the animals lacked an intelligence that human prey offered. This too contributes to Rainsford's internal conflict.