One of my friends' son was an e-athlete. At one point, he was one of the top 100 players of Fortnite in the world, and was up there for several other games, too. He took it very seriously. Since then, he's moved into the realm of "online personality" and makes a very nice living doing so.
Are you suggesting that it's not a sport if you can do it well past a certain age? If so, what age is that?
So, I guess while I wouldn't agree, if you are suggesting that a sport must be physically unsustainable, it would at least be consistent. I think that might limit "sport" to only a few activities that are high risk, and you'd end up with more exceptions to the rule than otherwise.
No golf, bowling, billiards, table tennis, tennis, angling, race car driving, or any activity in which one could continue to compete into their old age. I guess that BJJ would not be sport, either... nor would karate or many other martial arts. Baseball would be out, too. Right?