To be fair, that's just the more commonly-used definition.

By older definitions, doxing is simply the act of acquiring "dox" (documents) that contained information on a particular person. The mere act of doxing is generally something that is associated with the blackhat community. Unsurprisingly, it's largely become conflated with the idea of releasing private info obtained via doxing.

This is more or less a result of the terminology surrounding the release of doxed information, which is referred to as "being doxed". Which has lead people to erroneously conclude that "doxing" was the release of the information.

As for the legality of releasing personal information, it's not outright illegal in the US at least. Depending upon whether there's a clear threat intended, or whether the information released is public (NDA, database breaches, etc.), it very easily can be.

That being said, just because something isn't against the letter of the law, that doesn't mean prosecutors won't try to convict you. In any case, I'd think twice about trusting the average American to understand the difference and care enough about it to prolong the trial.

At least, that's my understanding of it.