I’m not sure you’ll find many who agree with you in this definition. The natural followup to “not meant to be public” is “meant by who?” Oftentimes people are doxxed through collation of various public records, kept and published by the government. I’m thinking things like phone books, arrest records, property transfer records, business registration, WHOIS registration, and many more. Then there’s times when the victim themselves didn’t realize they were leaking information. Even seemingly innocuous photos can be used by determined individuals to get a precise location [1]. I realize this falls under “unintentional” by your definition but would it be fair to say the person doxxed themselves in this case? I don’t think so.
To me the essence of doxxing is putting together otherwise disparate info into an easily sharable package. Something which raises the profile of the individual datapoints and their relation to each other until finding the victims information is trivial for anyone with a basic search.
1: See GeoWizards fantastic series doing exactly this: https://youtube.com/playlist?list=PL_japiE6QKWqMVC3JbyONau_0...