I have heard of this sort of holes token as arcade or a lot machine.
To add to the 'might never know' reality...there were a couple of die makers (Ingle & Orco) that had their name on machines designed use with scrip. They had exposed tubes for denominations with a device allowing individual tokens drop out! There are version I know of that have drawer and with just open divided fixed trays 'presumably' to hold coinage 'maybe' when taken in or tokens!
Anyway the registers are in same realm as those newspaper boy dispensers we use to carry on our belt.... Remember old guys?
My whole point of the register is to say there has been found a dollar size token with a substantial size hole (now I should know more & may ask someone to learn more) but the use thought to have been use as a very simple accounting device. Load tube with twenty tokens, dispense til holed token comes through then add more!
The Ingle register is very elaborate with stamped brass top "crown name plate type thing with their name", nice oak draws, a flat oak or marble flat piece under dispensing levers....I'll find a picture, wish I hadn't sold mine! The Orco is extremely more simple with denom tubes open....a picture will be added later!
So round & round the token you found is nothing like what I am telling about but it reminded me of it and somehow the round hole could have some comparable use?
Hope to post some pics later!
Mike