It's not an ad hominem. OP is saying that the person's entire job in writing such an essay is to think and make intelligent arguments about this particular area, and they have failed to do so in an obvious and silly way.

It's just like saying "embarrassing that $person is a firefighter and set their home on fire playing with matches" would not be an ad hominem.

An ad hominem would be: "embarassing that $person is a Harvard grad, making such an argument.", or "of course, we can expect such reasoning from someone writing an article for $publication"

Actually, an ad hominem is when you try to discredit an argument somebody made by attacking that person.

The example you cite seems closer to attacking a person based on their arguments being (perceived or claimed to be) bad. If you say "embarrassing an XY grad would make such a stupid argument" it will only discredit the argument if I believe XY graduates are stupid (I guess the $publication example aims at this). Meanwhile, if I don't see why the argument is bad and don't have a bad opinion of XY, your statement is entirely unconvincing.