This is the key thing now. Apart from places like GOG you don't really 'own' games. You lease a license, that can be revoked. Or in the case of the 'always online or have to connect to whatever server' you get that game until they kill the connect server, even on single player games. Steam is at least decent (for now) at keeping those still yours, but as mentioned all it takes is Gaben to no longer be in charge and it will go away too.
Some games still work and just give you that failed to connect, others are just dead and can't be played ever again. Some certainly still work after severs shut down but others are dead.
The days of decade plus old games still working is starting to fade away and it sucks.
Ubisoft thinks it's okay to delete your games library now apparently (gamerant.com)