These two men are professional hunters. It is in the hunt that they take pride. When Zaroff first tells Rainsford that he is to be hunted, Zaroff says,
"Your brain against mine. Your woodcraft against mine. Your strength and stamina against mine. Outdoor chess! And the stake is not without value, eh?" (page 11)
If Rainsford simply ambushed him, he wouldn't get the satisfaction of letting Zaroff know that he had been beat at his own game. Zaroff congratulates Rainsford in the end for winning the game. However, it was necessary to kill Zaroff. He wasn't about to let Rainsford off the island. Rainsford knows this. When Rainsford asked Zaroff what would happen if he wins, Zaroff tells him that he would be taken off the island, but he...
"....must agree to say nothing of your visit here" (pg 11)
Rainsford cannot agree to that. After all, Zaroff is killing human beings! When he tells Zaroff that he cannot agree, Zaroff says,
"Oh, in that case ----But why discuss that now? Three days hence we can discuss it over a bottle of Veuve Cliquot, unless...." (pg 11)
He leaves the ending open. Rainsford wins the game, and he has to have the satisfaction of looking Zaroff in the eye and letting him know who won. However, he knows he must kill Zaroff. He tells him,
"I am still a beast at bay" (pg 15) (last page of story)
The term "at bay" refers to an animal that is cornered and is forced to turn and fight. The reader has to respect Rainsford though. He could have just shot Zaroff and finished him off. Instead he challenges him to a dual with swords. Again, the most talented of the two men will win. Rainsford won.