It seems you want to screencast, something like chromecast I guess, but
interactive sessions. I do not know of any such program. I can think
of two hacks though.
You are right about that. The closest existing thing, as far as I know, is an Android device miracasting to a TV. Note, however, that the remote display is dumb, in the sense that for as long the remoting session is up, it will do nothing but show the desktop.