This was messing with my head for a minute, I thought maybe they had figured out a way to use mini CDs (like the GameCube) to make that tiny disc drive functional, but it appears to just be decorative.
The disc could then just be a caddy for a micro SD memory card, which when inserted on the disc slot would promptly launch a game stored in there.
Selecting games from a virtual library never has the same kick as when you insert a cartridge or a dis[ck] into a machine and have it boot from that.
Edit: I also realized you may as well cut out the memory card and just have each "fake" disc encode (perhaps optically) a little ID which the machine could read (perhaps a cheap camera) and associate to a game already stored in the machine's internal memory.
Mini-CD would be too big for this size, wouldn't they ?
Something similar to a credit card would fit the bill and could look gorgeous.
The issue of course would be that there aren't cards of that format that can store the amount of data required, but maybe with a bit of fantasy a micro-sd card could be embedded in it.
Yeah a minidisc is 64mm, I couldn't find the exact measurement in the README and can only dig so far on my mobile but even just eyeballing it and measuring a deck of cards it would be a lil too big.