Also, since when have trolls reacted like that?
I'm not sure what you mean here,
that is in fact how he reacted.
Anyway, the thing is kind of complicated. Rawlings did harass Mary Beard, under his own name. It seems weird to say Beard is not allowed to tell her followers on twitter that someone sent her a message calling her "a filthy slut". Even though that has the predictable consequence that, her being a public figure, a ton of harassment will fall against Rawlings in turn, it's not quite doxxing.
If his address had been posted publicly it would have been going too far. But that did not happen, as far as I know (someone offered, but he apologised before it happened). I'm not a fan of turning internet mobs against people, but the problem with that is that it means public figures are being held to higher standards than private individuals when it comes to saying "hey, this asshole harassed me over twitter".