I have this exact set (also in black and white), but I got it from a local antique store in Los Angeles and there was no identifying information. I believe it is made of stone resin.
The only information that I have found came from a facebook marketplace post of someone else who was trying to sell a similar brown and white version that they acquired at an estate sale (also in Los Angeles). I'll post photos from that Marketplace post (I copied them). My set is in storage and I don't have photos at the moment.
If the box is to be believed, the set was Made in Italy.
I know he got it around 1948, before or, when, he was in the U.S. marine core. I do not know where and cannot find any close matches looking through the web. Any info would be great thanks!