Sellers have an incentive to lie in many places these days, but sadly I am no expert on telling bone and ivory apart. I just have an interest in the CITES process.
The yellowing and cracking suggests some age and that the pieces are made of some material like ivory. Here is a CITES document on identification, none of it can be done from a photo. https://cites.org/sites/default/files/eng/resources/pub/E-Ivory-guide.pdf and here is something less technical https://www.realorrepro.com/article/Ivory-genuine-fake--confusing
I wonder at the knights all cracking but the rooks (also quite thick) not. The patina is uneven: compare the two bishops, on the left-hand bishop there is no yellowing where the fingers would touch it, and on the right it is quite yellowed, you might ask if they have been cleaned. The two rooks, which have carving all over them and which might be harder to clean, are more consistently yellowed. Keep in mind, I am no expert, just habitually paranoid.
Sorry I can't really help with your question.
Seller lists it as a bone set. @greghunt ?