Row-less layouts with columns are indeed quite common in the non-web world - see for example newspapers or other dense text. But that can already be done with current CSS features, and the row-first placement makes this proposal completely unsuitable for that. Masonry actively makes that worse, because it screws with the regular reading order.
They argue that nobody is doing it because it can't be done in CSS. I would argue that nobody is doing it because it's a bad idea. We've seen people work around it not being in CSS by using Javascript to make galleries for years now, if there were other use cases they'd surely have done the same?
With the exception of Pinterest-style galleries (and lets be honest, that's not exactly the pinnacle of UX either) I really don't see a widespread use for this feature. Their three other demos sure aren't convincing me.
The argument is that the popularity of the layout in contexts where it's possible is a strong argument for enabling it on the web as well. This is not a layout that they just thought of and are trying to invent.