What, ultimately, is “the most dangerous game”? Does "game" refer to the hunted ("game animals"), or to the competition between Rainsford and Zaroff? Or both? Does that change the meaning of the story?

The "most dangerous game" would refer to the game between Rainsford and Zaroff. Zaroff's most dangerous game was a hunter (Rainsford) who understood the act of hunting, and could thus, understand and anticipate Zaroff's moves. Rainsford was the most dangerous game. I do not believe this changes the meaning of the story.

Does Richard Connell appear to condemn hunting or condemn hunting animals—or both?