You say that, but after reading half of this HN discussion, after being a Redditor for many years, after consulting two dictionaries, and after googling "doxx", I still have absolutely no idea what that "precise definition" is. In fact, I have no idea what the word is supposed to mean at all, other than from context.
If only it were so simple. 'Doxxing' has some pretty obvious connotations that a more precise (if also a bit more verbose) description of what happened does not have. It has also first and more frequently been used in certain contexts (e.g. users of some website searching for and revealing personal information about other users of that website) while not in others (e.g. investigative journalists revealing personal information about people in their stories), so it doesn’t really translate well if applied everywhere.
Just to make that clear, I think Gawker was wrong in revealing personal information, but I think that’s more a general disagreement with journalistic ethics and culture in the USA. There personal information is in general much more often and frequently revealed than where I come from (Germany).