The island has an evil reputation what role do you think it will play in the story?
Your question involves "foreshadowing," which is a hint or clue from the author about what will happen in the story. In this case, the island's evil reputation is foreshadowing the importance of the island in the story, alerting the reader to the idea that the island is going to play a big part in the story and that that part will involve evil.
As Rainsford and Whitney discuss the island's reputation and the sailors' characterization of the island, the reader can see that Rainsford is dismissive of the island's reputation, characterizing it as "pure superstition." Whitney, however is not so sure, and as the reader sees these two points of view, most readers will speculate about whether Rainsford, with his dismissive attitude, is someone who will be harmed by the island.
Since this is a rather short story, and the discussion of the island and the men's dialogue occur in the beginning of the story, most of us can see that an evil island is going to be important and that Rainsford is going to have to eat his words!
In the opening scene of “The Most Dangerous Game,” Richard Connell’s use of violent imagery foreshadows the upcoming conflict by his description of the island and its evil reputation. Rainsford hears the shots off in the distance, and as he falls into the ocean he hears the cry of what he thinks is a hunted animal.
As Rena Korb says in her essay, The Most Dangerous Game”: Spare, but Not Simplistic, “The sea has become a place of violence, and the island, which represents his only chance for safety, promises more of the same.” For Rainsford, the island becomes a place of true terror, not the safe haven that he sought.