The difference lies in the fact that a really popular spectator sport mostly comes from a game people have already played at some point or could naturally conceive of(e.g. auto racing as an extension of driving, MMA as an extension of street brawls), and therefore don't need explanations for. Although Counter-Strike has a huge legacy among video games, it hasn't entered the school curriculum like baseball/basketball/football AFAIK, and it's only loosely related to a kind of live combat scenario that few people witness in person.

There's a step-function there where if a major educational institution started pushing a video game, it'd have the awareness to be a sport. But they don't, so the path forward is tied to the whims of the market.

It may work out that the 20th century pro sports model is just not going to be part of this. That model came from an era combining fast travel, broadcast media, and a small number of large sponsors. At first it was teams who travelled by rail and had their games casted over radio. Later, jet planes and TV. But nowadays, with the streaming model, it's diffused to being able to watch live speedrun attempts, an activity which can resemble watching paint dry at times, but which does bring in some income within a long-tail niche audience.