I CALL BS!
This is very cute, but (as in all failed satire) I can't tell if the authors actually believe this, or are pulling our legs.
The GAME our distant ancestors played was "merchantile commerce", played in the flesh with real caravans of sheep, ores, humans, lumber, textiles, etc.
Those tokens have already been researched as the prototype for cuneiform writing. They are, indirectly, the ancestors of our alphabet A,B,C, etc. A started as a little Ox head (since rotated to stand on its horns). B as a little house ("basa" iirc), C as a little Camel, etc.
Ancient merchants exchanged ownership by passing around these tokens in little bags. Eventually the bags converted to clay pouches, with a copy of the tokens stamped on the outside. And those stamps lead to written language.