So called "visual" programming languages like LabVIEW and Visual Basic seem to come very close. There's a supervisory program that manages and parses inputs, and schedules the invocation of functions when those inputs change. I'm not sure what those programs do with the outputs of functions is exactly what the author proposes, but you could let the supervisory program route the outputs of functions to their desired effects.
Definition of the expected input format and its interpretation, and likewise for the output format, would presumably be done in some meta-programming language.
My Visual Basic programs contained little or no input/output code, until I started using VB to control industrial machines.
I think this article is quite clearly just reprsenting idea for people working with functional side and maybe thinking something similiar already. So if you "cannot get it" and author cannot give ~easy answer don't judge yourself or the idea/author too much but accept that idea can be still very early phase and work-in-progress.
In the meantime, Dhall is much further ahead, so you could check out more of Gabriel's stuff if you need more convincing.
As I expected though, most people in this thread don't get it, which is understandable since it's pretty out there compared to the mainstream. I think they will once larger, "real" programs are written.
I don't think I'm gonna be able to "reword" this for people here so it suddenly clicks, you're probably just going to need to see it in action to understand it.