Japanese chess sets like this one are not antiques and quite modern as these things go, the quality of this set is not the best, but it is genuine ivory. The carved ivory pieces in this set are marked “Made in Japan,” which generally dates them either just before World War II (1939) and the early 1950s when trading relations resumed after the war. A great many will carry a makers “chop” (the artist's mark) inscribed on the base, but the majority of these markings are undocumented. One should always be careful buying sets of this vintage, as a great many are not actually ivory, but made of various forms of resins, grained and colored to look like ivory. You can test for ivory using a red hot needle, a hot needle will melt into most fake ivory materials and generate a hot plastic smell, but will not melt genuine ivory.
Most sets like this were made for the export/tourist market, their quality ranges a great deal, but few have the fine detail of sets made during the late 19th century. These pieces were not mass produced in the modern sense, but were made in great numbers and brought back by armed forces personnel, sailors, and businessmen right through the Vietnam War years. In the current market comparable sets to this one often sell at auction in the $300.00- $600.00 range.