With both the screen and the battery being chosen with their impact on environment in mind, you are probably wondering what about the remaining components, especially the microcontroller?
The quick answer to that is that the chip shortage has cleared any old micrcontrollers from the warehouses quite well already, so there isn't really much surplus we could draw on here.
The more detailed answer is that the main and overriding goal of this project is to remove as many obstacles between you and the game you are going to write, as possible, and the older microcontrollers simply don't have the resources, in terms of memory and speed, to run a Python interpreter. They often don't even have native USB peripheral on them, which means you would have to muck about installing toolchains, compiling your programs, and using special dongles and programs to flash them onto the device. This is simply unacceptable.
As for the other components, they are really generic, and you could easily use recycled ones if you are building this by hand. But for producing hundreds of the devices, the additional effort in hand-placing them and doing quality checks to make sure they work, with added risk that they might stop working at any time anyways, is simply not worth it.
So we will have this mixture of old and new technology — ancient screen with a advanced microcontroller, traditional battery with a modern voltage regulator, generic switch with new capacitors.
Oh, and I also looked into using paper PCBs, but it seems the technology is not quite there yet.