I don't see how it's any different from a public figure saying they'll be attending any public event.
I know people wish this weren't the case, but your address isn't exactly private information. Anyone can find it easily for anyone else.
So the bar for doxing is definitely a low one, but in this particular case it isn't met. I can see why Musk is irritated that that account exists, even more so because it didn't go away at the first request by someone as powerful as him, and that makes it personal. See the whole saga with that diver for a typical response. But that doesn't mean that the person manning that account is doing something illegal and that is the bar which Elon Musk himself set not all that long ago, and which is what makes this news.
If he had been a bit smarter about this he would have just said: "I'm irritated by you, this is my site and you're gone". That would be that. But now there are all these logical pretzels why this is illegal and all that other stuff that people - and Musk - do on twitter is not because 'free speech'. The two are incompatible, and he knows it.
Posting your home address which you've kept out of the public eye is doxing, posting the whereabouts of any aircraft that broadcasts that information to all receivers is not. That's why you can find this information all over the internet, the only place where you currently can't find Musk's jet is on Twitter. And that's before we get into his free-speech arguments which apparently were a bit inconsistent.
Or would you like to accuse the FAA of doxing as well?