But you can now use them even if the phone is turned off, unlike previously where the "web" devices just provided a view of data from the phone.

The Signal desktop client has always continued to work even when the phone was off.

Yeah, the implementation described in the article seems almost exactly how I understand Signal has been doing it all along. It's purely a client software choice not to allow a phone to be a secondary device. There's a fork which adds this feature to the Android app, though I forget what it's called.