On: Russia’s Retro Lenin Museum Still Runs on Decades-...

[Aloha]

The Apple II is one of a few computers that you could build a brand new one from parts if needed, they're not complex machines.

[boznz → Aloha]

or run on an emulator

[Aloha → boznz]

the article makes it clear that you need to interact with special cards to control the exhibits

[rdc12 → Aloha]

That problem could probably be solved using an FPGA (or even simpler tech)

[emilfihlman → rdc12]

Given the specs, an AVR could do it.