This is a great question that gets to the heart of what kind of person Zaroff is. Some context is important first.
Before Rainsford says that he does not feel well, Zaroff is explaining to Rainsford the new "game" he created. Zaroff divulges that he created a new animal to hunt. At first, Rainsford is intrigued, but when Zaroff says that this new animal is man, Rainsford is disturbed.
Zaroff explains that it is quite fine to hunt humans, especially the humans he has. There are nobodies, according to Zaroff. After this conversation, Zaroff wants to show off his collection of head. The intimation is that these are human heads. In view of this, Rainsford feels sick. However, Zaroff thinks that Rainsford is sick because of his swim.
Here is the point: it does not enter Zaroff's mind that Rainsford might be sick at Zaroff's custom of hunting humans. This shows that Zaroff is insane. Here is the quote:
"Ah, indeed?" the general inquired solicitously. "Well, I suppose that's only natural, after your long swim. You need a good, restful night's sleep. Tomorrow you'll feel like a new man, I'll wager. Then we'll hunt, eh?