Let’s forget about the larger discs, since I only have two. And I see no rectangular tiles with no holes. So let’s concentrate on the 73 discs of diameter 55 or 49 cm, which were carved from turned cylinders and all of which use a common iconography. You are postulating a game played with items that were obviously time-consuming and therefore expensive to make. In any complex economy you need a means of exchange to function, and to facilitate barter for food and commodities. For games you just need rules, and simple tiles made from cheap materials.
The critical thing with currency is that it is rare, and cannot be faked. It doesn’t have to be metal or shells. There was clearly a local source for this pseudo-turquoise, which I have shown is a unique form of microcrystalline calcite and dolomite, in other words a tertiary mineral formed by reheating and cooling. It then needed to be carved, for which carvers had the monopoly. You only need to postulate that they were under the control of the Hongshan ‘Government’ that also controlled the place where the material was found.
And no, you cannot assume that just anyone could get hold of the material. In fact we do not know where the material (either pseudoturquoise or glass) was found. Come to that we don’t know the location of the Hongshan jade or the agate deposits, maybe because they have been exhausted.
The glass was not MADE, it was FOUND. It is a natural pure silica glass, which must have been localised to a particular locality, since it was caused by a very particular impact, probably on the Gobi desert. What I do know is that the glass is still being mined, but now wasted - see my book and my lecture on Youtube. I am desperate to know where the mine or quarry is in order to test my twin craters impact theory, or come up with another candidate impact.
Finally, The Hongshan Culture’s economy depended on believing that there was an afterlife, for which objects cherished in this life could be buried with your body for use in the next, so there would be no mystery about being buried with your ‘money’ if you regarded it as a possession, just like your jade collection, for continued use in the afterlife.