In "A Piece Of The Action" the Iotians as 1920's gangsters were a spoof, an exaggeration of a stereotype perpetuated in 1930's films. And in "I, Mudd" we see the androids act in an exaggerated manner of how such things might be seen in B movie sci-fi. And note that in "What Are Little Girls Made Of?" and "Requiem For Methuselah" androids are not depicted in such an exaggerated way.
Those are standard comedic devices, why not just identify them as comedic? The only thing I see that might
qualify as camp are the over-the-top performances the crew puts on for the androids in "I, Mudd."
Basically, anything that isn't "dark", with characters wallowing in constant "angst" and "Daddy issues" is dismissed as "camp". "Fun", an characters who act like actual people is not allowed.
This view is incorrect. These stories have their place, and I can enjoy them on occassion, but now pretty much EVERYTHING has become that. And it has become tedious.
The use of the word is also incorrect, as far as the dictionaries I have access to.
Going back to the OP: All shows age, and all will look dated to younger viewers to some extent. TOS happens to be the eldest Trek. If a viewer doesn't have enough to identify with or connect to, they won't like a show that's so different in look, style, pacing etc. from what they're used to. With that in mind, TOS is quite remarkably ahead of its contemporaries in the amount of attention it generates, going on 50 years later.