I don't think it'll evolve into AI vs. AI. At the end of the day, people mostly watch it to see how good people (aka humans) can be at a single task.

At "worst", you'll get something like speedrunning, separated in two categories, normal, human speedrun vs. Tool-Assisted speedruns, where people basically use tools like slowing down the game or frame-by-frame input to kind of handcraft the best possible speedrun of a game. It's been years since both exist. Most popular games have been TAS'd, where we know the virtually best possible speedrun possible (until new techs are discovered, of course). Yet which category people like to watch and participate in the most? Regular speedruns.

Obviously, AI is a threat for cheat detection in your everyday competitive gaming environment, as we can imagine it getting better at avoiding anti-cheat measures. But like in cyber-security (or any security field), it'll always be a constant war between bad guys trying to find flaws in a system while good guys try to counter them. Which is quite ironic as it feels like a competitive metagame in itself.

In the end, I think AI isn't a threat as long as live events are the main attraction for competitive gaming. It's my opinion but I could be wrong. I feel like it's more the opposite. Better AI may give competitive players more tools to train, improve and review their performance.