Can't watch the video right now, but having thought about post-apocalyptic computing it seems to me that the biggest challenge is storage, both in the form of RAM and non-volatile.

You can build a reasonably performant CPU using a thousand relays or less, but storing bits takes a surprising amount of transistor-replacements. We're so spoiled with our giant caches and DRAM.

Hence why early computers used a lot of more analog ways to store data, like delay lines[1], core memory[2) and such.

[1]: https://en.wikipedia.org/wiki/Delay-line_memory

[2]: https://en.wikipedia.org/wiki/Magnetic-core_memory