The irony is that a lot of games before the era of centralisation have active preservation communities and will probably live on - but a lot of newer games likely won't, for the reasons you described.
I think it's very likely people will still play Tetris, Final Fantasy IV and Star Craft in 50 years. Star Craft II and Final Fantasy XV? Not so much.
Life, uh, finds a way. As long as you have talented people that love a game, they will find some way to preserve it. Even though Blizzard is still running Battle.net to this day (bless them for that) -- people have created spin-off servers for Starcraft by analyzing the netcode and mimicking the servers:
If Blizzard ever shut down battle.net 2.0 there will be a group of people putting their heads together to mimic the server. Or, if needed, recreate the entire game engine from decompiled code or scratch. Look at OpenRA and OpenBW for these examples:
And if that's not good enough, game preservation might become a new industry just like art preservation. We already have GoG releasing classic titles by working with publishers and digital rights holders to re-release classic games; this model can be extended to those "black box" games where the server code is saved in a repository for years but never released until someone like GoG comes along and revives the game the legal way:
Exactly right, we're looking at a hole in modern video game archival history with the way the industry models their games these days. The older games aren't nearly as hard to preserve.
I think it's very likely people will still play Tetris, Final Fantasy IV and Star Craft in 50 years. Star Craft II and Final Fantasy XV? Not so much.