An internal conflict is a conflict within the character himself. An external conflict is a conflict a character has with nature or another character in the story. It is clear in this story that the main conflict is an external conflict, but both are represented.
The internal conflict in "The Most Dangerous Game" is when Zaroff becomes bored with hunting animals. He has become quite skilled at capturing all types of animals on the island and wants something more challenging. As a result, he turns to hunting humans on the island and it becomes a game for him.
Another internal conflict is when Rainsford is struggling to stay calm during the hunt. There are a few instances when Zaroff has figured Rainsford out but chooses to let him live longer to make the game more fun and interesting.
The main external conflict between Zaroff and Rainsford is between each other. Zaroff informs Rainsford that he lives and the island and hunts man. He informs him that this is a game for him. Rainsford's conflict is the ability to try and stay alive. As a result, the only way that he will get off the island is if he kills Zaroff. Only one character can live in this story, and Rainsford is determined that it will be him.