I'm not the first to think of this but how about this for an Olympic sport:
Aerial combat with contemporary aircraft but with laser guns so that when you get your first hit on your opponent his throttle becomes limited to 75%. next hit 50% and then 25% and then the throttle is cut. This is all done above 10,000 feet altitude and when you are "shot down" and descend below 10,000 your engine will function again.
I believe many of the original Olympic sports were based on warrior skills so why not this one?