Question

What does the phrase sporting proposition mean the most dangerous game

Answer 1

I think that the phrase "sporting proposition" means a game of chance. 

It was used in this dialogue:
"Simply this: hunting had ceased to be what you call `a sporting proposition.' It had become too easy. I always got my quarry. Always. There is no greater bore than perfection." (1.96)

When you say "sport" is infers a chance of winning and losing. There is no sure outcome.
In the above lines, hunting has become a sure deal and it does not invigorate nor inspire the hunters to do better.