Richard Connell's "The Most Dangerous Game" illustrates both internal conflict (man verses self) and external conflict (man verses man/nature, man verses supernatural is not present).
Man verses Self
When Rainsford first realizes the truth about the "game" he is playing, he becomes very frightened:
Then it was that Rainsford knew the full meaning of terror."I will not lose my nerve. I will not."
This understanding of fear and talking himself out of losing his nerve speaks to the internal conflict Rainsford feels. It is his own courage fighting his own fear.
Man verses Nature
Both Zaroff and Rainsford face the external conflict of man verses nature. Zaroff's supremacy over animals on earth is illustrated by his need to move onto something far more challenging.
"No animal had a chance with me any more...The weak of the world were put here to give the strong pleasure."
Although the quote refers to Zaroff's inability to find any animal that could reason, it illustrates his search of nature for a being which could. Zaroff had to move on from animals and take up the sport of hunting mankind.
Rainsford, on the other hand, is forced to face the jungles and Zaroff's hounds. Both elements of nature, he finds it necessary to kill the dogs (with the Burmese tiger pit) and put nature to his use (when climbing the trees for protection and making the traps).
Man verses Man
The greatest conflict of the story takes place between Zaroff and Rainsford. Zaroff, wanting to hunt an "animal" which can reason, has turned his attention to men. Rainsford, unfortunately, has literally washed up onto his island. Given Rainsford's renown as a hunter, Zaroff wishes to challenge him. Both men intend to kill the other in order to survive.