This is man VS. man because General Zaroff and Rainsford both fight each other and it becomes clear that Zaroff is the Antagonist.
Rainsford has to survive in the wild for at least 3 days so that he can beat Zaroff. He also has to fight off General Zaroff's dogs.
When Rainsford was at the last couple of days of trying to survive Zaroff, he decided to jump into the ocean and he had to decide if he wanted to. So Rainsford had to battle himself to try to make that decision.