The reason that General Zaroff came to this island was so that he would have some place where he would be able to hunt human beings.
General Zaroff tells Rainsford that he had hunted every kind of animal. He had tried every animal that was supposed to be smart and hard to hunt. He did this because he wanted a challenge. But every single one of those animals disappointed him. None of them was smart enough to challenge him. So he decided to start hunting people and he bought this island so he could do that. Here is the relevant quote:
I needed a new animal. I found one. So I bought this island built this house, and here I do my hunting.