pose. 

Zaroff is aware of Rainsford's reputation as a hunter. When Rainsford arrives at Zaroff's chateau, Zaroff tells him:

"Perhaps," said General Zaroff, "you were surprised that I recognized your name. You see, I read all books on hunting published in English, French, and Russian. I have but one passion in my life, Mr. Rainsford, and it is the hunt."

He is aware that Rainsford is a talented hunter and will be a challenge for him. To this point, Zaroff has been hunting sailors that become shipwrecked on his island (by his own design). He complains to Rainsford that they do not challenge him.  He is able to kill them too easily, and as a result, he is suffering from boredom.  Being bored by the activity that was once his passion is greatly unsettling.  Hunting Rainsford, who will be difficult to kill because he knows all the strategies and tools of a skilled hunter,  gives him hope that he will restore his passion for the hunt.

Zaroff's "game" is the hunting and killing of human prey on his island.

Zaroff is a former Russian aristocrat who takes singular pleasure in hunting as a lifelong passion. Unfortunately for him, he has become bored with it, because he has hunted every animal worth hunting and found none of them to be a match for him. In his opinion, no animal can match a hunter with a good weapon and his wits about him. Therefore, he decides that humans are the only animal capable of giving him an interesting hunt, because they are rational. Yet Zaroff once again is disappointed because he finds that his usual lower-class prey, culled from wrecked ships, is not mentally astute enough to match him, and he remains unbeaten and rarely challenged. 

Zaroff is excited for Rainsford to play this game because Rainsford is a famous hunter, and therefore Zaroff assumes that Rainsford will know how to make the game interesting for him, specifically by anticipating his plans, hiding his tracks and, apparently, fighting back. 

Sangor Rainsford only agrees to be hunted because if he does not, he will be turned over to Ivan, who will undoubtedly torture and kill him.

While General Zaroff talks with Rainsford at dinner, he mentions the lack of enthusiasm for hunting that he had until he created his "dangerous game." But now, he complains, this "ennui" [boredom] seems to be returning because the hunting the night before was not exciting. 

"The fellow lost his head. He made a straight trail that offered no problems at all. . . . It's most annoying."

Since Rainsford recalls having heard the pistol shot, he is well aware of the outcome of that hunt. So, when Zaroff suggests that he and Rainsford hunt that night, Rainsford shakes his head in dissent. "No, general, . . . I will not hunt." Zaroff shrugs his shoulders and replies that the choice is Rainsford's, adding,

"But may I not venture to suggest that you will find my idea of sport more diverting than Ivan's."

Rainsford recalls the general's description of Ivan as once having served as "official knouter" to the Great White Czar." (He issued whippings to criminals.) According to Zaroff, Ivan "has his own ideas of sport." General Zaroff also has mentioned that the others who have been on the island have invariably chosen the hunt. So, since not agreeing to the hunt as suggested by Zaroff means a prolonged and brutal death, Rainsford decides to be hunted by Zaroff. As an accomplished hunter himself, Rainsford figures that he may be able to outwit Zaroff. 

First, one must understand that Zaroff is a bloodthirsty savage as the story's antagonist. He likes hunting people in the first place, as he considers them the ultimate predator/prey combination.

Once we understand that, it stands to reason that he would be excited by the prospect of hunting Rainsford, who himself is a professional hunter. Rainsford, in Zaroff's mind, represents the pinnacle of human prey -- he can use skills that the average person does not possess.

Rainsford doesn't really have much choice in the matter. The evil General Zaroff's got him over a barrel, so he's not in a position to refuse. He must become the quarry in his next human safari—he risks being tortured by Ivan, otherwise. At the same time, Rainsford, being a hunter himself, understands Zaroff's mindset. He knows just how thrilling the chase can be.

Although Rainsford has never actually participated in hunting human prey himself, he might be curious to find out just what it's like to be the hunted rather than the hunter for once. Rainsford likes a challenge, and this could certainly be the biggest challenge of his life. (And the last, if Zaroff gets his way). Of course Rainsford would rather not be in this position, but as the saying goes, if life gives you lemons, you make lemonade. Maybe Rainsford could use this deadly hunt as an opportunity to dig deep and find hidden strengths he never even knew existed.