I don't think they're paper, the embossing on paper (cardboard) chips is more like thin lines whereas these chips have large areas of relief.
These are certainly vintage, 30s-40s sounds about right. Some research might nail it down more definitively, but undoubtedly these are old. Old doesn't necessarily mean rare, desirable, or valuable, though.
The're probably plastic, but "clay" chips are actually plastic, so the description isn't necessarily wrong. "Clay" chips are a blend of mostly plastic with some clay minerals, and almost all poker chips from that era are that sort of clay / plastic blend. The alternatives would be ivory, bone, wood, paper / cardboard, or a few types of plastic such as celluloid, Bakelite, or Catalin. Later on chips started being made of newer plastics such as acrylic.
It's hard to know just from looking whether chips like the ones pictured are "clay" (a mix of plastic, usually celluloid, plus some clay) or Bakelite (a different kind of plastic which can also but not necessarily contain binders such as clay).
You can see some more examples of old chips like this - as well as several other types - here:
https://www.antiquepokerchips.com/SeymourGuide.htm
The particular chips you have are included in this guide! See
https://www.antiquepokerchips.com/2013/Animals&Reptiles.pdf , page 4, "PA-GE Lucky Elephant Embossed". Unfortunately, just seeing the picture doesn't really tell us much that we don't already know. There probably isn't a lot to say about them, though - I don't know if anyone has, for example, conclusively identified a manufacturer or a time period. But they are old, and nobody has made anything like them in quite a long time. If you think they're interesting and you like they way they look, then I think you should be happy and enjoy your purchase!
