Square pieces is definitely not what I was thinking, but a great idea!
Although those pieces are pretty small pawns maybe 200 mm tall max, I was imagining 2 to 3 times that size.
What you really need for DIY is a 4 axis cnc router and some foam blanks, although it could be done a large wood lathe for most parts.
There I am thinking cylindrical again....

must be the beer glass..

What about 32 acquired witches hats with fancy tops where required..