Many sports require full-body coordination. I would also consider, say, a skilled ballet dancer much more obviously impressive and intriguing than being the best video gamer in the world. The only reason one might not consider it a sport is that it's not as competition-oriented (and I may be completely wrong in that; I can't feign deep knowledge of ballet).

I don't think it's disparaging to not consider video games a sport, either, it just seems like a category error. Much of the skill is simply not visible to people not intimately familiar with the game, the mechanics, and what might be difficult about it. I would put it in the same category as, say, live coding, or watching an expert artisan at work. I also can't fathom, say, the skill it takes to operate a crane as a world-class expert, or ice carving, or fixing a mechanical watch, or blowing glass.

Frankly, I also don't consider most streaming to be a "real" job. But that's probably related to the fact that I don't respect most content that emerges. But you could say the same thing about podcasting, or being an opinion columnist, or a pundit/talking head. This doesn't mean it doesn't take skill or effort; I just think it's not producing much of value.