I think they're making the claim that if we're looking at "varience", variety, etc. then pf1e has more overall variability. Pathfinder does it with a combination of classes and archetypes, where 3.5e does it with just classes. I don't think they made the explicit claim of there being more classes in pf1e by overall number.
I find that instead of pathfinder having more "classes" by number, it feels more honest about what is a class and what is a subclass/archetype. Imo, many 3.5e classes would be archetypes in pathfinder, as they fit your definition of "instead of x, you get y" without much substantial difference. And likewise, in my experience playing different archetypes in pf can produce vastly different player experiences (some archetypes and classes more than others, for sure).
All of this is pretty subjective, though... and I personally haven't heard anyone making fun of 3.5e for lacking classes, compared to either pf1e or 2e, but it could happen!