Other than colors, that looks identical to a set my mother made for me back in the 1970's or early 80's at a local ceramic studio. She made it from molded greenware (unfired clay) and hand painted it. She made a few of these for other chess playing family members & friends, using different color combinations.
While the story you state is nice, I'm sorry to say it seems likely to me that the set in your picture was made in a similar fashion to mine, instead of being acquired in a trade from an officer in the Russian Navy.
Update: A similar set is now on display at the World Chess Hall of Fame. The first molds for sets like this were probably created in 1960's or 1970's by a company then known as Duncan Ceramics Products. As long as the link is good, you can see the set on display and read more at: