Given that there are pro chess players who are also pro competitive gamers, I doubt the gap is nearly as big as you are imagining. The skill ceiling for some video games is
extremely high. I would in fact be unsurprised if it was possible to objectively compare difficulty and come to the conclusion that there are competitive video games which are significantly harder than top-level chess. I realize this sounds ridiculous, but the breadth of competitive gaming is very large, and many video games have extremely huge meta games, come down to millisecond-level reaction time differences, and so forth. There's even a physical aspect, as a lot of video games can put immense physical stress on specific muscles. I think most people think of the bigger spectator games, like Fortnite or MOBAs and the like, but those games are not necessarily the upper echelon of eSports; plenty of niche games make for very interesting competition. Like NES Tetris with CTWC even! NES Tetris is mostly about solo execution, but there are other puzzle games, such as Puyo Puyo, which is maddeningly difficult to become even casually decent at, and has a huge sprawling metagame in versus matches. Then there's fighting games. So many fighting games. The interactions between matchups in fighting games have made for such interesting and divergent strategies that games literally nearing 30 years old are still having their metagame evolve through innovations in play style, honing in execution, or even just very carefully studying game mechanics.
(Note: I am not suggesting there are necessarily CURRENTLY video game competitions where the top competitors are as "skilled" as top chess players, but chess play has had much longer to evolve than any video game. That said: due to the internet, I do think skills of average players has gone up much more rapidly than historically, and I am just suggesting there's likely games with similar or perhaps higher ceilings, with top competitors in a similar wheelhouse. This especially since video games can take advantage of more kinds of skills due to the technology.)
It's easy to write off pro gaming, but in my opinion, it's full of surprises. Honestly, I think you can even forget about only competitive gaming and alone; a surprising number of people tune in just to watch people "speedrun" video games solo. The art of speedruns or speed demos is probably one of the most fascinating subcultures, and the amount of work poured into the "perfect" run is completely unfathomable. Maybe even crazier to me that people just do it for the love of the sport.
I think the "spectator sport" potential of video games mostly has to do with how fun it is to watch rather than how high level the competition is. The latter can help, especially if you have competitors with running storylines, but let's face it: a huge part of it is the game itself (some games are very amusing to watch, like say, Rocket League) and the audience's connection to it.
I don't really think it's hit the ceiling. In fact, I agree with the notion that it is limited in large part due to the tensions with business models. You can see this very clearly with Nintendo, a company notoriously bad at community outreach and sparring with their own playerbase. Even if their games were not the best competitive gaming experiences ever, it feels like they often can't reach their potential in large part due to legal issues, and that is probably not too uncommon. Valve and Epic Games seem to be a lot better about supporting their respective communities, but it still feels like by and large, there is a growing tension in eSports and it has little to do with the games themselves.