How is General Zaroff's character believable?

General Zaroff is believable because his actions mirror his surroundings and because some of his actions subvert the expectations a reader would have for a cruel, old man who hunts people for sport.
The jungle where Rainsford arrives after surviving the turbulent ocean mirror one aspect of General Zaroff's personality; it's harsh and unyielding. It doesn't conform to normal human standards. When Rainsford reaches the house, however, it shows another aspect of Zaroff's personality: that of the older, polite, sophisticated man. Because the reader is already plunged into Rainsford's surroundings, they're prepared for General Zaroff. Because he fits into the setting, he's believable. The dichotomy of the setting echoes the dichotomy of the General and makes him a more believable character.
Another thing that makes him believable is the subversion of expectations when Rainsford meets Zaroff. At first, the interaction with Ivan builds suspense -- but then Zaroff welcomes him. He appears to be the kind of person who is civilized and not like a murderer. This also helps him appear more believable. Because he isn't immediately introduced as a hunter of humans, the reader has a chance to get Zaroff's measure before the more difficult side of his character is introduced.

Professional writers have long used a standard technique of creating believable characters by giving them one outstanding trait and one contrasting trait. In the case of General Zaroff, the author has made him a sadistic, merciless man who has grown bored with killing animals and now gets his pleasure and excitement by hunting and killing human beings. Such a man was necessary for the plot of "The Most Dangerous Game." But in order to make his character believable, the author, Richard Edward Connell, has given General Zaroff the old-world manners of a polished aristocrat. This helps to make him seem three-dimensional. He is exceptionally polite, considerate, amiable, polished, generous, intelligent, and well-educated. He treats Rainsford with kindness and courtesy, even though he is planning to kill him. Both sides of Zaroff's character are believable. It is possible for wicked and cruel people to have very good manners. Zaroff may not even feel any hatred for the beasts and humans he kills. He seems to have a high regard for his captive, Sanger Rainsford, just as big-game hunters often appreciate the beauty, grace, and courage of the animals they kill. What is lacking in General Zaroff is a sense of right and wrong. He cannot really empathize with the feelings of others. Perhaps he is devoid of feelings himself, which would make him a sociopath. Some sociopaths are said to be exceptionally likable and charming. This makes it easy for those of them with killer instincts to victimize others and to keep getting away with it for a long time.