The setting of "The Most Dangerous Game" is essential to the story. Without this specific setting, we would not have the same story. Explain why. How does the setting affect the story? Additionally, why is the setting perfect for General Zaroff's game? Be specific and use at least one citation.

It is correct that with a different setting the story would not be exactly the same. However, I do not think that the setting is entirely what makes this story work so well. The 1994 movie Surviving the Game is essentially a movie of "The Most Dangerous Game." A few things have been changed here and there, like setting and character backstory, but the core remains the same. It is a movie about skilled hunters pitted against each other in a hunt to the death.
What the movie and the story both do similarly about setting is place events of the story in remote locations. This works incredibly well for "The Most Dangerous Game" because Zaroff needs a place to hunt humans that is far from prying and curious eyes. He cannot just have anybody wandering onto his hunting grounds. Additionally, Zaroff's island essentially makes it impossible for any man to escape him.

The smile on the general's face widened. "To date I have not lost," he said. Then he added, hastily: "I don't wish you to think me a braggart, Mr. Rainsford. Many of them afford only the most elementary sort of problem. Occasionally I strike a tartar. One almost did win. I eventually had to use the dogs."

If the hunt was on the mainland and the hunted was fit enough and fast enough, the hunted could essentially just keep running away. Zaroff would eventually be taken so far from his home that continuing the pursuit would be too much trouble. Setting the story and Zaroff's home on an island contains his prey. He has his own confined battle arena in which to go to work. The Hunger Games has a similar setup. Additionally, the island gives Zaroff access to prey that will not be missed. Sailors go missing for various reasons. They can fall overboard, ships can get lost, or they can run aground. The sailors' death is more or less expected in those cases, so when Zaroff captures and kills them, nobody cares enough to investigate. Zaroff says the following:

If I wish to hunt, why should I not? I hunt the scum of the earth: sailors from tramp ships—lassars, blacks, Chinese, whites, mongrels—a thoroughbred horse or hound is worth more than a score of them.