If your map has a channel drawn in the left side of the island in the Caribbean Sea (with the Atlantic Ocean on the right-hand side), then Rainsford swims ashore near this channel which has jungle on the left of it, fringing the shore, and cliffs with jagged crags to the jungle's left. Deeper in the interior of this island is the chateau that belongs to General Zaroff. Having invited Rainsford to dine with him, Zaroff suggests his "dangerous game," and he cautions Rainsford to avoid the Death Swamp that is located in the southeast corner of the island. This location is told to Rainsford while they dine shortly after Rainsford has made his way there, hoping to attain help.
Therefore, on your map, you will wish to draw Death Swamp in the lower right-hand corner of the map of the island. In this swamp there is deadly quicksand, so the general suggests that Rainsford avoid it.