In one instance, the word "game" can mean a competition. As it relates to the story, General Zaroff is playing a "dangerous game" in hunting humans. Actually, hunting in itself is a dangerous "game" or sport.
In another use of the word, "game" can refer to an animal that is being hunted. Small game hunters go after animals like rabbits or fox, while big game hunters seek elk, deer, or lions. Rainsford could be "the most dangerous game" that General Zaroff has ever hunted. Rainsford is himself a hunter, so he knows various traps he could set to keep Zaroff away from him. Also, humans in general could be the most dangerous game because, unlike jaguars, humans can think and strategize.