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.