Richard Connell's "The Most Dangerous Game" is set primarily on an isolated Caribbean island on which there is only one structure; that mansion belongs to General Zaroff. Sanger Rainsford is only on the island at all because he accidentally fell overboard from a yacht he was sailing. He was on his way to a hunting expedition, and very soon he will be forced to apply everything he has learned to save his life.
General Zaroff appears to be a civilized man who is living in isolation, surrounded by opulence of every kind. He has the best books, the best clothing, and the best wines and foods; he even hums the best music. He is a big-game hunter, and he has the heads of all his greatest catches mounted on his walls.
Over a very civilized dinner, Zaroff reveals that he has grown bored with hunting animals and now hunts humans. It is a horrific thing to contemplate, and Rainsford is understandably appalled. He is even more horrified to learn that he is the general's next prey. If Zaroff does not catch (and kill) him, Zaroff promises (on his word as a gentleman, of course) to take Rainsford wherever he wants to go. The specific rule of the hunt, as set by Zaroff, is this:
"I'll cheerfully acknowledge myself defeated if I do not find you by midnight of the third day," said General Zaroff.
Rainsford eludes (or is deliberately allowed to live) Zaroff for several days. On the third day, Zaroff brings his dogs with him, and Rainsford has no choice but to jump off the cliffs and onto the rocks below. Zaroff assumes, of course, that Rainsford is dead, and he goes home satisfied.
At ten o'clock that night, Zaroff locks himself in his room as he prepares for bed, and of course we know that Rainsford survived the fall and is now hiding behind the curtain of Zaroff's bedroom. When Rainsford shows himself, Zaroff is of course surprised.
The general sucked in his breath and smiled. "I congratulate you," he said. "You have won the game."
Rainsford did not smile. "I am still a beast at bay," he said, in a low, hoarse voice. "Get ready, General Zaroff."
The general made one of his deepest bows. "I see," he said. "Splendid! One of us is to furnish a repast for the hounds. The other will sleep in this very excellent bed. On guard, Rainsford." . . .
He had never slept in a better bed, Rainsford decided.
These are the last lines of the story, and your question is a good one. The "beast at bay" comment refers to the fact that it is not yet midnight, so Zaroff's admission that he has lost the game is not really true. The hunt does not end until midnight according to Zaroff's own rules; so Rainsford is still fighting for his own life and, by killing Zaroff, the lives of other unsuspecting human prey. Rainsford calls himself a beast at bay, an animal that is cornered by not yet caught, because it is not yet midnight of the third day and he intends to fight for his life.