I don’t get the relevance of that link, it talks about logical falacies like:

A: “All rodents are mammals, but a weasel isn’t a rodent, so it can’t be a mammal.”

I don’t see how that’s relevant, there is no way that can be seen as an ad hominem. The entire piece seems to be like that. And obviously ad hominem is not a logical fallacy as in flawed use of actual logic like boolean logic. And obviously explaining how and argument is wrong, is not an ad hominem. That’s normal discourse to progress on the issue.

But this part:

Therefore, if you can’t demonstrate that your opponent is trying to counter your argument by attacking you, you can’t demonstrate that he is resorting to ad hominem.

I believe I have CLEARLY shown that the comment “you are hurt and angry” is exactly that. If it’s not an argument based on his (wrong) interpretation of my person, then what is it?

From wikipedia which is way more concise, and actually talks about what an ad hominem is instead of what it is not:

https://en.wikipedia.org/wiki/Ad_hominem

Ad hominem (Latin for ‘to the person’), short for argumentum ad hominem, refers to several types of arguments that are fallacious. Often currently this term refers to a rhetorical strategy where the speaker attacks the character, motive, or some other attribute of the person making an argument.

In this case me being emotional.
If he writes, you are wrong because you have a big nose. That’s an obvious ad hominem. You are wrong because you are being emotional is an equally obvious ad hominem. They are the exact same fallacy as writing you are wrong because you are an idiot.