Depending upon the person, there are many definitions of the word "civilized" For our purposes we will use the definitions from the World English Dictionary of "having a high state of culture and social development" and from Dictionary.com of "having an advanced or humane culture; polite; well-bred; refined." Based on these two definitions, Zaroff would definitely believe that he is civilized.
His father was a very rich man with a quarter of a million acres in the Crimea. Rainsford notes that Zaroff has a "cultivated voice marked only with a slight accent" and that he had "the face of an aristocrat." Zaroff entered the military beause "it was expected of noblemen's sons." He is educated and well traveled as is evidenced by the fact that he has "read all the books on hunting published in English, French, and Russian" and that he has "hunted every kind of game in every land." When he left Russia broke, he made his own money by investing in American securities.
Zaroff is refined in that he has a servant, lives in a mansion with electricity, dresses for dinner in evening clothes and insists that his guests do the same, loaning Rainsford his own clothes. His suits are designer clothes made by a London clothier "who ordinarily cut and sewed for none below the rank of duke." When they met for dinner, Rainsford noted Zaroff had "the finest-the linen, the crystal, the silver, the china." Although Zaroff served champagne with dinner, he apologized to Rainsford for any lapses in "the amenities of civilization" as they were well off the beaten track. Rainsford was even "finding the general a most thoughtful and affable host, a true cosmopolite."
Finally, to Zaroff hunting was a sport. He was wealthy and did not have to hunt for his food. This kind of hunting was the sport of gentlemen and the aristocracy of Europe. It was the kind of hunting "civilized" and refined people do. He sees hunting as a game. As long as he treats the men he is going to hunt "with every consideration. they get plenty of good food and exercise. They get into splendid condition." he sees nothing wrong with the sport of hunting men.
Zaroff thinks he is civilized. However, we may not.