Your link seems to support the generic use of the word. The old gaming equipment catalogs describe it as celluloid, as a generic term. Maybe trademark enforcement is stronger in Europe than here in the U.S.? In the U.S. you can lose your trademark rights if the term becomes generic.

I have an old crate of ivory color celluloid in the basement, that came from a dice manufacturer. It's marked:

LUMARITE & CELLULOID
CELLULOSE PLASTIC PRODUCTS
Celanese Celluloid Corporation
Newark, NJ.
Demand the Original

So maybe "cellulose plastic" is more generic. For me, it will always be celluloid.