First, Rainsford must swim to save his life. Then Rainsford must avoid being killed by Zaroff. This is the main external conflict. Using his skills and knowledge as a hunter/predator, Rainsford tries to become an impossibly elusive prey. But this external conflict is inextricably linked to his internal conflict. Rainsford hunts and justifies this by saying that humans are superior to animals. Rainsford tells Zaroff that he does not condone cold-blooded murder even though he killed in the war. Zaroff also thinks humans are superior to animals because of his ability to reason. Both men claim justification for killing (animals and humans) based on superiority and/or a civilized reason.
Rainsford survives (his external conflict) by becoming the hunter of Zaroff. By the end of the story, we get the impression that Rainsford is, or has become, more like Zaroff than he might like to admit. In his simplistic view of the world as hunter and "huntee," Rainsford chooses to be one of the hunters. The question that is left unanswered is if he has learned anything in being one of the huntees (prey). He sleeps in Zaroff's bed and this suggests that he is exactly like Zaroff and has therefore learned nothing. Looking at the story as a whole, with the savage context of "kill or be killed," this is Rainsford's external conflict: kill or be killed, or "survival of the fittest." The conflict shows the murderous potential of humanity and this hardly justifies the notion that humans are superior to other species.