That is extraordinarily unlikely. They are almost certainly polypropylene or polyurethane.
I'll bet it is melamine resin. My set from China (that my wife got me) it just that. Similar to Bakelite, but not quite as dense.
Do a Google search on "melamine chinese chess" and you should find something suitable. Get a good wood board - if you just get the pieces you probably get a thin cheap paper fold up board that won't last the first spill/sneeze.