I've never hated Comic Sans, and still don't. But there's no question in my mind that it was overused, and -- worse -- often used inappropriately.
In-between, after Apple bundled Zapfino making it accessible, and before Google Fonts made Lobster accessible, it was Zapfino that was abused everywhere.
I have always hated Times New Roman. I am alone in the world.
They're referring to the font, yes. Lots of people used it in the post-Web 2.0 era because it has a "distinctive" look, which naturally lent itself to fatigue.