Life and death are the stakes of the "game" that Zaroff plays. I think this is certainly true. This concept is implied in the title along with the several other more direct meanings of the language of the title.
It's impressive to see how many ideas can be pulled out of just a few well-chosen words!
As a matter of fact, there is a double entendre to the entire title: the most dangerous game involves the tracking and struggle with the most intelligent of the hunted, or game: man. In addition, this very hunt of man as the beast of prey is, indeed, the most dangerous of games.
Yes, I do. It's hard to escape the double meaning of the word "game" in the title. It obviously refers to the sport of hunting as well as the target to be hunted. Put "most" and "dangerous" in front of both meanings and you have the plot of this short story.
To answer your question, "Yes!" There is little doubt that the author, Richard Edward Connell (1893-1949), carefully titled his classic short story, "The Most Dangerous Game," with the intentional double meaning. As you have mentioned, the title refers to both the hunting of humans as the prey--the hunted--and to the act of hunting being like a game or contest. As prey, the human is far more dangerous than an animal because of man's greater intelligence; and as a game or contest, it is a far more dangerous proposition because of the social and moral implications involved with hunting a human being--and the resulting penalties that may result if the human hunter is caught by the law. Connell adds yet another possible twist to his story: The fact the hunted human may be able to elude his human hunter and turn the tables on him, as Rainsford did to Zaroff.