The Fallout setting when the bomb drops is a sort of alternate future where technology evolved oddly after the 1950's. So it has a 1950's + futuristic vibe. The bombs are dropped in 2077.
It is the alternative world in wich micro processor was not a thing (no internet, no micro chips, no digital era), while vacuum tube, EM and nuclear tech went fully advanced. Thus 2077 looks like this. TV show is not adaptation of exiting game. Instead it is like a new game that comes about 9yrs in time after latest game. Meaning they didn't go an easy way like TLoU, and instead created new story, plot, characters, while staying true to Fallout franchise.
