One of the skills expected from a CEO is initiative. Person who would fit as a CEO is expected to know how to contact Stack Exchange and present themselves in a proper way.

That's why, to my understanding, they don't post a direct form, which would likely only cause hundreds of joke/unfitting submissions, and it will just waste lots of time to SE staff who will need to wade through it all.

So yes, they look for new CEO. They want the best of the best to apply. Good luck! :)