Hmmm well I think it might be a limitation in targeting web techs for the output. Because of that, you are at the whim of the technology itself and how it handles multiple windows.
So for example, you can create a "popup" in a web browser but there is a disconnect there from the child window to the parent window that construct would have to handle. Construct doesn't support this right now that I am aware of.
Now consider that on mobile, how would you even achieve that kind of popup?
Now consider desktop with NWjs. NWjs would have to support opening a new window which might be possible but then Construct would again have to deal with the new child popup window.
It's not really an easy problem since the deployed platform controls so much about the windows container that the construct instance live in (i.e. Desktop, web browser, mobile).
The Multiplayer side of things is probably still the way to go for a realtime second screen. Could even have your main screen on your computer and then have the second screen on a tablet using that method.