Aircraft are all publicly tracked. All this account did was create a bot to take the info from the FAA site and post it to Twitter.
Whether you are finding someone's email, or real name, or jet location, or home address, and then announce it, you are doxxing them.
We used to have a thing called the phone book that put everyone's name, phone number, and address together in a book and sent it out. None of those is a piece of private information.