Even clay chips are made out of plastic.
Almost anything made out of plastic is a composite of multiple materials, including one or more polymers (what we might notionally think of as "plastic") plus plasticizers, fillers, reinforcements, and colorants. One of those fillers can be clay.
The particular formulation of the composite is what gives any particular composite its properties, including the way it feels. The composite formulation for whatever plastic is being used for these chips (or any others that advertise themselves as "clay", "clay composite", "real clay", "true clay", etc) may or may not include clay, and if they do include clay, it may or may not be present in sufficient quantity to have any significant effect on the way the composite feels and behaves. There's not really any way to know. Presumably there's enough there that if sued by the Fair Trade Commission or some similar agency for false advertising they'd be able to prove that their claim is
technically correct, but honestly that's a pretty thin presumption. I'd be prepared to bet that there's not a bit of clay contained within any of 'em, and they're relying on a) not being sued or otherwise called to task by anyone over it and b) being prepared to claim that "clay" has no standard definition within the context of poker chips (which is true!) and that it can legitimately be used to describe any chip that resembles in any manner any chip that has historically contained clay.
But the bottom line is that none of that matters. No matter how much clay these sorts of mass-market injection-molded plastic chips do or don't contain, they are completely unlike the sorts of chips that people
think they are when they hear "clay" - i.e. they're completely unlike the clay chips (which are also made out of plastic) that are widely used in casinos. They're not made from the same materials, they're not made in the same way, they don't look alike, they don't feel alike, and while quality is subjective almost no one thinks that the injection-molded plastics are anywhere near the quality of casino clays.
Thanks for the links! I definitely have some questions about the construction methods.
Ask away! ... either here, or in a separate thread if you prefer. The PCF membership is here to help.