This quote is taken from the end of the story. When Zaroff tells Rainsford that he is about to be hunted, he tells Rainsford that if he wins, which Zaroff thinks is doubtful, he will have his sloop drop Rainsford off at the nearest town on the mainland. The only condition is that Rainsford
"must agree to say nothing of your visit here." (pg 9)
Rainsford says that he cannot agree to that. That changes the rules of the game, and Zaroff says..
"Oh, in that case ---- But why discuss it now? Threee dys hence we can duscuss it over a bottle of Veuve Cliquot, unless...." (pg 9)
Rainsford knows that Zaroff cannot let him live because he cannot let anyone know what he is doing on Ship Trap Island. A "beast at bay" is a hunted animal. The hounds hunt the animals and the barking sound that they make is called "baying". Therefore a "beast at bay" is an animal that is being hunted by hounds. Rainsford knows that he cannot just win because Zaroff cannot allow him to leave the island. Therefore he is still being hunted, and he is a "beast at bay". The only way to win is to kill Zaroff and that is what he does.