Here is my somewhat theoretical take. Hunting dangerous game in the classic sense is shooting an animal that is dangerous, and then dealing with the consequences. In archery, and in a lot of modern booked hunts, you only do the initial shooting, you don't stop the animal that may die right away, or press home an attack. Barry Wensel, Paul Schaffer, have "seen the lion" so to speak, and settled maters with a bow. I am not too sure what opportunities really exist to do that kind of hunting with a bow. Hogs might be an example. Not overly tough, but something one could reasonably feel good about trying to stop with a bow, and some fancy footwork.
I am not saying there is anything wrong about being in on shooting a lion, or buff or whatever you want. But it is only dangerous game if you are the one sorting out the danger. It would probably be plenty dangerous to take the first swing at an Heavyweight, then jump out of the ring and let a pro settle the rest, but I don't think that is boxing.