In short, the new animal that General Zaroff decided to hunt is man. The more important question is why Zaroff created this "new animal."
When Rainsford met Zaroff, Zaroff seemed to be a sophisticated and generous host, even if a few things about him seemed odd. As Rainsford got to know him better, he found out that Zaroff was fond of hunting. In fact, he read many of Rainsford's books on the subject.
Zaroff was such an accomplished hunter that he wanted more of a challenge. So, he created a new game and animal to hunt. Hunting people for a challenge was Zaroff's invention. Here he is in his own words:
"Simply this: hunting had ceased to be what you call `a sporting proposition.' It had become too easy. I always got my quarry. Always. There is no greater bore than perfection."
The general lit a fresh cigarette.
"No animal had a chance with me any more. That is no boast; it is a mathematical certainty. The animal had nothing but his legs and his instinct. Instinct is no match for reason. When I thought of this it was a tragic moment for me, I can tell you."
In conclusion, because Zaroff was bored and wanted a greater challenge, he started hunting people. In the end, he would meet his match in Rainsford. The hunter became the hunted.