The setting helps establish a mood and foreshadows the plot.
In the beginning of the story, we are already getting details about the island that Rainsford is passing by—none of them good!
"The old charts call it `Ship-Trap Island,"' Whitney replied." A suggestive name, isn't it? Sailors have a curious dread of the place. I don't know why. Some superstition--"
They go on to have a discussion about the island that includes Rainsford getting a bad feeling about the place. It is unclear at first what is so bad about it. Are there cannibals there? Even cannibals won’t go there. So that would indicate that the island is not inhabited. Or is it?
This discussion foreshadows the dangers on the island and the dangers in store for Rainsford since he is the one with the misgivings. He also separates himself from the group. Unfortunately he falls into the water and ends up washed up on the island.
Dense jungle came down to the very edge of the cliffs. What perils that tangle of trees and underbrush might hold for him did not concern Rainsford just then. All he knew was that he was safe from his enemy, the sea ...
He has no idea things are about to get so much worse!
The island itself, other than being remote, also literally can trap a ship with its giant rocks. This allows Zaroff prey, because he tricks ships into thinking there is a channel. Its rocky shore means few passers-by will stop there either. In addition, it is ideal for hunting because of the trees, bogs, and swamps. All of this makes the game of murderous hide and seek possible.
This island is necessary for the plot of this story. Its events could not as easily have happened anywhere else. A sociopath like General Zaroff would have been caught and arrested on the mainland, when the people he was hunted would have been noticed missing. Also, it is necessary for Rainsford to be on a ship at the beginning of the story so that he can end up on the island in the first place. The ship needs to pass the island so that he can fall off. Passing the island allows us the conversation gives us information about the spooky nature of the island and that foreshadows the trouble that will happen there.
The gripping tale of a hunter who falls off a ship and ends up in a nightmare with a deranged man who hides on an island and forces him to be his prey is much enhanced by the island setting and the foreshadowing on the ship. The author creates suspense and drops hints early on to keep us guessing, right up until the point when Rainsford wins the game and the hunter becomes the hunted once more.
The setting of any story sets the tone. If we keep this in mind, an island that is inaccessible to people is the perfect setting for the short story, "The Most Dangerous Game."
Let me explain further.
Right from the beginning of the story, a tone of suspense and danger is set. Rainsford and his friend are in a remote place to hunt. As they are on a boat, they see an island in the distance and Rainsford asks about it. His friend, Whitney, says that it is called "Ship Trap Island." This name itself gives a sense of foreboding. It is a place of danger where even experienced sailors should not tread, but this is exactly where Rainsford is. Here is what the text says:
"OFF THERE to the right--somewhere--is a large island," said Whitney." It's rather a mystery--" "What island is it?" Rainsford asked. "The old charts call it `Ship-Trap Island,"' Whitney replied." A suggestive name, isn't it? Sailors have a curious dread of the place. I don't know why. Some superstition--" "Can't see it," remarked Rainsford, trying to peer through the dank tropical night that was palpable as it pressed its thick warm blackness in upon the yacht.
As the conversation continues, the foreboding of the island grows. Here is what it says:
"The place has a reputation--a bad one." "Cannibals?" suggested Rainsford. "Hardly. Even cannibals wouldn't live in such a God-forsaken place. But it's gotten into sailor lore, somehow. Didn't you notice that the crew's nerves seemed a bit jumpy today?"
As we read these words, one thing is clear: danger and perhaps even death awaits. So, when Rainsford falls off the boat and goes to that island, we know that he will have trouble. All of this is implied by he context of the boat and island. A perfect setting, indeed.