I doubt you'll be able to nail it down any further than you already have. Listings for items like this (sets of mother-of-pearl game counters, or simulated mother-of-pearl game counters) show up on
eBay from time to time, but they're generally speaking one-off items from a variety of sources, manufacturers, materials, quality, and age. If the box doesn't have any identifying features on it such as a legible name or date you probably won't be able to identify it.
If you keep a close eye on the
eBay listings you might eventually see one that looks identical, and that could tell you more about it.
Even if you don't find one that's identical, you'll see some that are
similar, perhaps similar enough to give you some idea of what it's worth. It looks quite attractive to me; a nice case, overall in good condition, genuine mother-of-pearl, and very nearly a complete set. A set like that is somewhat uncommon.
