What happens with your Steam Machine if Steam decides to pull the plug for whatever reason?
Yes, that's a pretty shallow promise not a guarantee. If they don't, there's always piracy to get access to the games you already legally purchased.
So, realistically someone would make a tool to do this automatically (not done now because API changes quickly, which is not an issue at EOL).
The larger issue is multiplayer servers run by Valve. Some games allow you to run a server and connect to arbitrary servers, most do not. Those are going to be somewhat unplayable without explicit action from Valve.