Toward the end, after Rainsford jumps of the cliff, Zaroff sits and smokes his cigarette while humming a tune from an opera. Why would he do that?
Zaroff does this because it fits in with what we have seen of his personality -- it fits in with the image he has of himself.
Zaroff thinks that he is a very civilized man and an aristocrat. He thinks that his "game" is the ultimate expression of this -- that he is so superior that he can treat human beings as animals.
So what he is doing here is relaxing after having enjoyed a very satisfying hunt. He has gotten a big challenge from Rainsford and (he thinks) won. So now he's going to relax. When he does so, he's going to do it with style and class -- humming a tune from an opera.
So, it's like coming back from playing a nice game of pickup basketball, sitting back, relaxing and drinking a soda or something. But it's much more sophisticated and the game was much more deadly than basketball. That shows us that Zaroff thinks he's more sophisticated than average people and on a higher plane, because he plays the most dangerous game.