General Zaroff thinks of himself as civilized for two reasons. First, he has all the trappings of aristocracy -- nice clothes, a butler, a fine mansion with a hunting preserve. Second, he sees hunting as a very civilized pursuit (as it is seen by, for example, English aristocrats).
His lack of civilization is best evidenced by the very fact that he purposely causes shipwrecks in order that he can hunt and murder the people who wash up on his shore.
What is civilization? You can ask yourself which is more important -- having material goods that look civilized, or acting in some way that we see as moral. Then you can ask yourself if anyone in this story really is moral and whether Rainsford is civilized or not.
There seems to be a general tendency among people who exploit others to think of themselves as being better than those they exploit. A prime example was the aristocratic men and ladies in the South in the days of slavery. They thought of themselves as being exceptionally genteel and refined in order to excuse their vicious conduct. It was true of the ancient Romans and the Spartans and of the British who ruled India. They had to think of themselves as being superior in order to excuse the injustice of their domination of others. Zaroff is a typical aristocrat. He considers himself "noble" and must therefore walk the walk and talk the talk. He is really a hateful person who conceals his wicked, selfish, sadistic characters under a mask of refinement.
He believes he dresses and acts liked a civilized person, but in reality, he savagely causes shipwrecks so he can hunt the poeple he had captured.