You are talking about online games here which are a subset of games. And I agree they exist in the moment since they rely on external servers and other players.

Most games aren't online games though and those would realistically last forever if it wasn't for companies shutting down activation servers or download servers. There's also a problem where old games get delisted. If you want to play an old game today you can just buy the disk of ebay. Now the only way to buy a game is through the digital store which won't be selling the game forever, with no way to officially transfer copies between players.