The setting of "The Most Dangerous Game" is very important to the tone and mood for the story. Given that the story takes place on a relatively unknown island, Ship-Trap Island, only rumors circulate about the island. The rumors which circulate are negative ones--sailors tend to try to stay away from the island. This is brought to the attention of both the reader and Rainsford (the protagonist) by Whitney:
"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--."
Knowing this dread of "the place," Rainsford is most certainly apprehensive when he finds himself on the shores (after falling off of the boat he was traveling upon).
Once in Zaroff's home, Rainsford's apprehensions continue given the unknown state of the island and the "game" Zaroff plays. Therefore, the setting of the island affects the mood and tone of the story given that Rainsford has no clue what is to come because of his lack of knowledge of the island itself. Not only is Rainsford unfamiliar with the island, he is also unfamiliar with both Zaroff and his type of game. The hunt which takes place is embellished by the obscurity of the island itself.
As a suggestion, when writing an essay on the topic, one would need to examine the quote named at the beginning ( of this answer) in order to establish the curiousness of the island itself. Outside of that, one would need to focus on the curious happenings which exist on this unknown island. The obscure nature of the island feeds into the obscure game played (and, therefore, the tone and mood).