Childish really is the best word for it.
It wasn't a measured, intelligent response. It came across as a "beat the journalist up" because they posted a bad review. Reminds me of the sort of thing you see bad restaurant owners do when they respond to diner's complaints.
I disagree completely -- a better analogy would be that a restaurant owner gets pissed off because the reviewer complains of a fly in his soup when circuit cameras reveal this was never the case.
It wasn't that Broder simply disliked the car. Musk felt he had falsified data to make Tesla look bad.
It will make some people rally to his cause more, and it will turn some people off (likely the ones who wouldn't buy the cars anyway).
If you wanted to criticise the response you could call it cynical, but I think you'll agree that's a long way from being childish.