Which type of conflict dominates Connell's "The Most Dangerous Game" and why?
The previous answer does a good job in pointing out that the main conflict is between two men, but I would add that the main conflict is between two hunters.
In the beginning of the story, Rainsford, the protagonist, and his friend, Whitney, are discussing hunting. Within this conversation Rainsford says that the world can be broken down into two classes. The hunter and the huntee. Connell takes this classification and runs with it.
When Rainsford finds himself on the island, he meets general Zaroff, a veritable sociopath, who invented a new game to satisfy his boredom. In short, he hunts humans. Eventually Rainsford is forced to play this game, and he becomes the huntee. This situation does not last for long. Rainsford realizes that this stance is a sure way to die. So, he goes on the offensive. By doing this, two hunters come against each other in conflict.
This point takes general Zaroff by surprise. He does not even consider that Rainsford would do this. This is precisely why he is shocked when Rainsford is waiting for him in his own house.
From this perspective, we do see a dangerous game of life and death between two accomplished hunters.
Now as to why Connell does this, we don't actually know for sure, as the story does not say explicitly. However, we can take an educated guess.
The story is about hunting. So, the most exciting match would be between two hunters.
While revenge, arrogance and social prejudice are prominent themes of Connell's "The Most Dangerous Game," the main conflict revolves around man vs. man. This is a story of pitting two experienced hunters against each other in a contest to see who would out-wit the other. General Zaroff uses dogs, weapons, and his knowledge of the island (man vs. nature) against his adversary, Rainsford, in order to create the most epic hunt ever. And the actual hunt itself is not the only conflict in which the two men engage; they also argue before the hunt about whether or not General Zaroff is committing murder rather than a playful hunt. Obviously to the hunted, it's not anywhere near playful.