what different meanings does the word “game” have in the story?

Well the word "game" has a double meaning here. There is of course the game of the hunter and the hunted. Then there is the type of animal being hunted that is dangerous. That would be an animal that can reason being human. Just from the title, I didn't get the full meaning of the story. As soon as Rainsford got into Zaroff's castle, I clued in.