This post-apocalyptic world where people are able to play video games doesn't sound very post-apocalyptic. If I still have the electricity to power a game console then it sounds more like post-annoyance.
Not that hard to get electricity. The switch would be easier than a standard home console. All you would need to do is have something to charge your system. Whether its actual electricity working, a car batter, generator or whatever. You would have electricity far longer than you would have a stable internet or internet in general.
But Switch, you just need to charge switch and you can play for hours. Others you need to have the system have constant electricity as well as a constant electricity for the TV. Or two big batteries/generators/ect to keep them running.