Indeed, Rainsford has learned what it means to be "a beast at bay." He has learned what fear is, and he understands what Whitney meant when he spoke of the fear that the jaguars would feel as they were hunted. So, now he appreciates all that fear entails--being hunted, terror that one may be caught, knowing that one must fight back in order to live. Now, perhaps, he perceives that life itself is truly a hunt in which the strong always conquer the weak. Life itself is "the most dangerous game" in which a person is involved, whether the threats be physical, psychological, or social. Perhaps, then, Connell tells his 1929 Great Depression audience that man has always been "a wolf to man" as the Russian proverb goes.
When Rainsford climbs to the room of General Zaroff and tells his foe that he is still "a beast at bay," he means that he knows he will never be rid of Zaroff as a deadly predator. Rainsford really has no choice but to kill Zaroff, or he will never be able to leave the island. For, Zaroff will continue to hunt him and then kill Rainsford himself; after all, he plans to go out for Rainsford the next day and surely must want revenge for the loss of Ivan and a dog.
One way to answer this question is to say that Rainsford has learned nothing of value, certainly nothing of ethical value in terms of the sanctity of human or animal life. Rainsford never really has a profound change of heart about killing. Although forced to protect his own life, he does play Zaroff's game, killing the dog, Ivan, and finally Zaroff. In the end, the narrator states:
He had never slept in a better bed, Rainsford decided.
Presumably, Rainsford kills Zaroff, gives him to the dogs and then sleeps in Zaroff's bed. The narrator doesn't say that Rainsford has never slept so soundly or after such a relief at having saved his own life; it is not a sleep of getting out of Zaroff's game. Rainsford decides that he has never slept in a better bed, as if the bed were a reward from the hunt. It's as if he feels not only justified but empowered at having defeated such a worthy adversary/prey as Zaroff. In this sense, he is no longer appalled at Zaroff's sport of hunting people. Rainsford has just played this game as well. And by killing Zaroff, and taking his place, he becomes Zaroff. The hunted becomes the hunter, and takes his reward.
Zaroff comes across as a civilized, cultured man, but the reader soon discovers that he is racist and he uses that civilized rationale of superiority to kill animals and people. His justification is simple and cold. He is strong, they are week; therefore, he is justified in killing them. This strikes at the notion that modern civilization has allowed humanity to rise above any primitive or instinctual violence; meaning, in this story, "civilized" species are just as violent as wild species. Given the title, one suggestion is that humans are more violent ("most dangerous") than any other species.
Zaroff compares what he does to war. Rainsford stops him saying that war "Did not make me condone cold-blooded murder." Again, the civilized argument, this time from Rainsford, is that war is necessary killing but killing for sport is not (A bit hypocritical considering Rainsford kills animals for sport, because he, like Zaroff, thinks he is superior to them). Both men use the duality of superior/inferior to justify killing. Certainly, there is an argument to be made here about war versus murder, but it does show how the so-called civilized minds will find justifications when they think killing is necessary. Note that earlier in the story, Rainsford tells Whitney that animals don't understand that they're being hunted and therefore they don't suffer fear. Rainsford then resorts to the duality that the world is made up of the hunters and the hunted, foreshadowing Zaroff's equally narrow-minded duality of the strong and the weak.
Given these reasons, Rainsford learns nothing new about the limited worldview of the duality: hunted and hunters. He does not renounce this narrow-minded way of thinking. One could argue that winning Zaroff's game only reaffirms his beliefs. The only value Rainsford might have learned is to feel what it is like to be the prey, the weak, the hunted. He may at last understand that fear and have some new understanding of sympathy for the hunted. But in the end, he still plays the game. In the end, he doesn't quit the game of murder; he continues to play it. He reasserts his role as the strong hunter, as the superior hunter, and therefore deserving of the superior bed.