The primary external conflict in "The Most Dangerous Game" by Richard Connell is the fact that Sanger Rainsford is forced to become the hunted; it is also this conflict which causes him to have at least some internal conflict.
Before he falls off the yacht and lands on Zaroff's island, Sanger Rainsford is pretty adamant about what he believes to be true. He tells Whitney, the ship's captain, to
"Be a realist. The world is made up of two classes--the hunters and the huntees. Luckily, you and I are hunters."
He goes on to add that animals lack understanding and therefore do not know anything other than being hunted as prey. Once he lands on the island and meets General Zaroff, however, Rainsford is forced to rethink this assertion.
Zaroff appears to be a civilized man in every way, and he is also a big-game hunter; at first, then, Rainsford thinks all is well. What he soon discovers, however, is that Zaroff has grown bored with hunting animals who have instincts but who cannot reason. Of course we learn that Zaroff has begun hunting humans, but even hunting the shipwrecked sailors is beginning to bore him because they are gripped with fear and usually rely on simple survival instincts rather than trying to outwit Zaroff.
When it finally becomes clear to Rainsford that Zaroff intends to hunt him or allow Ivan to torture him, Rainsford has his first internal conflict. He says:
"Hunting? Great Guns, General Zaroff, what you speak of is murder."
Though neither option is satisfactory to him, he must choose one. He chooses to hunt. That choice leads to many small internal conflicts, as he faces and overcomes his fears and is forced to fight to save his life. It is safe to say that humans are conflicted about being treated as prey; in the end, however, Rainsford gets the opportunity to turn the tables and become the hunter instead of the huntee. Though we do not see it or hear it from him, it is likely that Rainsford has at least some conflict over what he will do if he ever has the chance to kill Zaroff. In a civilized world, most people are unwilling to consider killing another human being. In this situation, however, Rainsford has come to the decision that he must kill Zaroff in order to save his own life--and the lives of others. It is not murder; it is self-defense.
The physical conflicts in the story all lead directly to Rainsford's internal conflicts.