The person vs. person conflict is most evident between Zaroff and Rainsford. Zaroff places Rainsford in a situation where Rainsford is the prey and Zaroff is the predator. It is a conflict in which Rainsford's life is at stake. Related to those two men is another person vs. person morality conflict. Zaroff sees no problem with hunting humans while Rainsford views Zaroff's actions as murder.
"Hunting? Great Guns, General Zaroff, what you speak of is murder."
The two debate on the topic for a bit before Zaroff decides to hunt Rainsford.
The person vs. nature conflict can be seen in Rainsford's struggles to avoid the dangers of the island itself. His jump off of the cliff is a good example of how nature could possibly kill Rainsford. He must also navigate the dangers of the jungle. Things like quicksand make his avoidance of Zaroff all the more difficult because Zaroff already knows about those places.
The man vs. obstacle conflict is centered on Zaroff and Ivan. Rainsford's disadvantage is that he doesn't know the island, and he has minimal weaponry; however, Rainsford is an excellent hunter with a vast knowledge about setting traps. Zaroff is able to successfully avoid those traps, but Ivan isn't so lucky. Ivan is killed when Rainsford's knife trap kills Ivan.
But the hope that was in Rainsford's brain when he climbed died, for he saw in the shallow valley that General Zaroff was still on his feet. But Ivan was not. The knife, driven by the recoil of the springing tree, had not wholly failed.