What happens when an Internet-heavy game, such as Switch Sports, loses its connectivity and most of its player base after a few years?

This is a problem with every online only game. Publishers could push an update for offline play (I think switch sports already has this) or a way for users to host their own server. But when a game is at end of life there's no incentive to push an update like this. It needs to be considered while the game is in initial development. Usually the server shuts off and the game dies. See Killer Queen Black for one of many examples. That game got removed from the store too, so even if you buy a physical copy you can't update the software to the newest version.

It's sad.