What exactly is your problem here?
"Let's make a clone of the working game to remove a few features and end up with basically the same thing"
In the premises of having a demo on Steam, having key auth for the DEMO means being able to play on Steam with your actual key, turning the DEMO into a full game. That's all. Having the whole auth on the Steam DEMO would be pointless and also allow people to auth with their keys.
If you would simply not make it being able to auth, there would be no point of the bottom auth bar, nor for networking or for the Network options in the menu.
What's so hard to understand in particular?