There's no such thing as a "tone" argument. Recall your freshman year Greek rhetoric course -- what are the three main elements of argumentation? Logos (logic), pathos (appeal to emotion), and ethos (morality or "greatness" of character).
If you start yelling at someone, chances are you're going to destroy your pathos and ethos. Being persuasive involves more than just logos, it involves convincing your audience that you are on the right side.
This, by the way, is why many technical people are awful at arguing. They don't understand that argumentation is about convincing people, not having a bullet point list that you haughtily defend to the last.
The real reason you're right is that the author was clearly adding a bit of dramatization and flair to the piece, rather than blowing up and insulting their opponent.
The "Tone argument" doesn't apply to the person who's being annoyed (they are not making a tone argument), but to someone who 'replies' to them.
Think of "tone argument" like "ad hominem", it's a reply to what someone says, but you don't actually respond or address what they said, instead you address how they said it in a very angry manner ("tone argument"), or based on what sort of person they are ("ad hominem")
