It would be pretty trivial to flatten a Casio - or equivalent tech - to this degree. The biggest problem would be battery thickness. If you didn't support charging or battery replacement you could fix that with a standard ultra-thin rechargeable battery and solar power.
OLED panels are less than 1mm thick, so the display wouldn't be a problem.
I'd honestly be more interested in that as a product than in a clockwork Veblen toy.