There are quite a few conflicts that the characters are faced with in this short story. Zaroff's major internal conflict stems from the fact that he no longer enjoys hunting animals. Zaroff's internal conflict is that he does not see the challenge in hunting animals and needs to find a more intelligent type of prey to hunt -- for him this prey becomes man. The internal conflict then becomes -- does he hunt man or does he continue to hunt something that he does not see a point in hunting. Zaroff obviously makes the decision to hunt man.
Zaroff's internal conflict is his conflict with boredom.
Zaroff is a very experienced hunter. He has hunted just about every major predator the planet has to offer, and he has been victorious. He's gotten so good at hunting that even the most dangerous of predators isn't a challenge for him anymore. Consequently, hunting is beginning to bore Zaroff.
"They were no match at all for a hunter with his wits about him, and a high-powered rifle. I was bitterly disappointed. I was lying in my tent with a splitting headache one night when a terrible thought pushed its way into my mind. Hunting was beginning to bore me! And hunting, remember, had been my life."
Zaroff says that hunting is his life, so the fact that hunting is starting to bore him is a major problem. Zaroff is essentially admitting that he is struggling with a purposeless life. He needs to find an exciting hunting challenge. His solution is to hunt humans.
"Oh," said the general, "it supplies me with the most exciting hunting in the world. No other hunting compares with it for an instant. Every day I hunt, and I never grow bored now, for I have a quarry with which I can match my wits."
Hunting humans reinvigorates Zaroff's passion for hunting, because humans offer what no other species can offer. Humans are able to reason.
"I wanted the ideal animal to hunt," explained the general. "So I said, `What are the attributes of an ideal quarry?' And the answer was, of course, `It must have courage, cunning, and, above all, it must be able to reason."'
For Zaroff, his main internal struggle isn't whether or not killing a human is right or wrong. His main internal struggle is avoiding boredom. Hunting humans is not a moral problem for Zaroff, because it allows him to avoid being bored.