The setting is Ship-Trap Island in the early twentieth century, a small Caribbean isolated island covered in dense vegetation with tall cliffs at one end and a beach on the other.
When you are making a story diagram, you want to be brief. Therefore, it is important to just point out the important elements of time and place. We know that the island is Ship-Trap, but we do not know exactly where it is. We do not know the exact time period either, but there are guns and Cossacks are mentioned, so we can guess it was the early twentieth century, or the 1900’s because Cossacks were soldiers in Russia around that time.
From Whitney’s comments at the beginning of the story, we know that the island is somewhere in the Caribbean.
“… I've seen you pick off a moose moving in the brown fall bush at four hundred yards, but even you can't see four miles or so through a moonless Caribbean night."
The island is inhabited by one man. You might also include that in your description. He lives in a “palatial chateau” on a high buff. The island is surrounded by cliffs, and there are dense trees almost everywhere. Since it is the Caribbean, seasons are not important.
Setting is important because this story really could not have happened anywhere else. Once on the island, Rainsford was trapped. There was no one for him to call, and no way to get off. He had to play the game, or die.