“Just distribute the server” isn’t a requirement. It has never been a requirement. Who said that’s a requirement?
It’s just a possible solution. And to me it seems to be the easiest since that is the exact way it used to be done.
What exactly publishers will have to do depends entirely on if the campaign is successful and how the resulting laws are written. And may be as simple as an expiration date on all future game sales.
Works with non-Steam games as well. I even had community profiles for Diablo 2. You just have to give the game the correct name and it should just work™.