Remember that external conflict is conflict that lies outside of a person's psyche and normally takes the form of conflict with another person, group of people or an institution. Therefore it is clear that the external conflict that General Zaroff faces is his hunting competition with Rainsford that he himself initiates. When General Zaroff says to Rainsford, "Tonight... we will hunt - you and I", he begins an external conflict that will be played out on Ship-Trap island and will be lethal for at least one of them, as both hunt each other to the death. This is the conflict that dominates the pages of this exciting and scary novel as we follow the narration from Rainsford's point of view and see how he tries to outwit General Zaroff and wins the grisly competition.
You have gotten an excellent description of external conflict, and I only have a couple of things to add. In "The Most Dangerous Game," the clearest and most obvious external conflict is with Rainsford in a hunter-huntee relationship. Another man vs. man conflict is with all those who were deliberately shipwrecked on the island and then hunted. One other kind of external conflict is man vs. society. General Zaroff is clearly in conflict with society--he has isolated himself on an island so he could capture and hunt humans. Nothing about that is acceptable behavior and would be punished severely in a court of law--putting Zaroff in considerable conflict with society.