Growth as some kind of synonym for quantified (how?) technological progress: I'm unqualified to answer but I suspect it has something to do with reconciling macroeconomics and the ecological concept of net primary production.

Growth in terms of $ equivalent, adjusted for inflation: even for the mere world of atoms, this is untrue. Global GDP roughly dectupled from 1950 to 2008 and there's no way that's solely attributable to digital services.