From Zaroff’s point of view, the key event is when he almost fell into Rainsford’s Burmese Tiger Pit because this is when he realized that Rainsford was a worthy opponent.
Zaroff is bored. He hunted the biggest and most difficult prey from around the world, but it was never enough. He was smarter than all of them.
Hunting was beginning to bore me! And hunting, remember, had been my life.
Zaroff solved the problem by finding the “most dangerous game”—man. He got himself a little island in the middle of nowhere, arranged for some ships to sink every now and then, and hunted away. Yet even these guys were beginning to bore him, until a skilled hunter showed up on his doorstep. He was thrilled. He realized that once again, hunting could be challenging.
Zaroff would have doubted Rainsford at first. When he came across the tiger pit, he realized that Rainsford was a worthy competitor and beating him would be a challenge.
"You've done well, Rainsford," the voice of the general called. "Your Burmese tiger pit has claimed one of my best dogs. Again you score. I think, Mr. Rainsford, …. Thank you for a most amusing evening."
Zaroff is not afraid. Life had become boring for him, and only the challenge interested him. He would rather risk his life against Rainsford than continue being bored.
Eventually, Zaroff loses. Yet he is happy just to have played the game. The game had become boring, and Rainsford made it interesting enough.
It seems that Zaroff's lack of value in human life extends to his own. He is not even interested in his own. For him, life is boring unless there is risk.