The other educator spells out where Connell explicitly states the geographic location of the yacht in which Rainsford and Whitney are traveling before the former man falls overboard, only to find himself on the mysterious Ship-Trap Island.

Other indications that the island is located in the Caribbean Sea include a description of the water as "blood-warm" when Rainsford falls over the railing. Since only tropical waters have warm water, this narrows down the possibilities of the location. Another clue is the description of the jungle on the island, a fact of the landscape that Rainsford noticed almost immediately after climbing onto shore from the rocks. This further supports the idea that the location is in a tropical environment.

Knowing that Rainsford is from New York City, as he says to Zaroff's doorman, the reader can infer that the tropical location must be somewhere close to the United States since the yacht was headed to South America.

This means that the Caribbean Sea is the only possible location in which Ship-Trap island could be within the context of the story. Even if one missed the sentence in which Connell names the Caribbean, all of these details would allow any reader to figure out the location.

Richard Connell's "The Most Dangerous Game" begins with the protagonist, Sanger Rainsford, on a yacht. The ship's captain, Whitney, is sailing his vessel in the dark past a mysterious and rather foreboding island which the sailors all refer to as Ship-Trap Island. 

The first hint we have about the ship's location is that the narrator tells us Rainsford looks out into "the dank tropical night," so we know we are in a tropical climate. When Whitneywatches Rainsford try to see the island, he tells the renowned hunter that

"even you can't see four miles or so through a moonless Caribbean night."

We know, then, that the yacht is sailing through the Caribbean Sea. 

Our last bit of evidence is their destination: the ship carrying Rainsford is on its way to Rio de Janeiro so Rainsford can hunt jaguar "up the Amazon" River.

It is evident, then, that Ship-Trap Island is in the Caribbean Sea.