1. In the story, it says that Zaroff's father was a wealthy man: "He was a very rich man with a quarter of a million acres in the Crimea... ."
2. General Zaroff was also an "officer of the Czar"--meaning he was a military man. This is also a source of income.
3. When Rainsford is putting on clothes offered to him by Zaroff, he notices that the suit "came from a London tailor who ordinarily cut and sewed for none below the rank of duke."