Not necessarily.
-snip-
Of course this is entirely unfeasible as each person would have to calculate the hash of a transaction and verify the transaction by hand whenever it receives a new one and that would take ages to do.
Well doesn't you statement agree with mine? Technically one could make it work but it would be so slow and complex that it would make zero sense to even try to keep it running (ergo answer is no). The Bitcoin network does not function without the internet and computers. Someone could try calculating, with the given hashrate in the video, how long it would take 1 man to find a block now. I would be interested in the answer.
Untrue. Here's a practical analog p2p network implementation, as conceived by Alphonso Tourette in 1869.
Relevance?
There question will be if some people will survive?
For you maybe; I could care less. OP was just curious I guess and I'm sure that OP realizes that Bitcoin wouldn't matter at that point.