The author seems to be advocating the photographic composition technique of filling most of the frame with the primary subject without discussing photographic composition in general. This is a standard approach for portraits, which are typically of humans posed in a sitting or standing position such that they're taller than they are wide. The term "portrait orientation" comes from this fact and indeed, the author's example of the Mona Lisa is a portrait.

It's no surprise that humans are more interested in portraits of humans than images of most anything else; we're a social species. A Google image search for "most famous photograph" also returned a portrait as the first result: Afghan Girl. Interestingly the first result for "most famous painting" is a squarish landscape: Starry Night. (Standard disclaimer about this not being a scientific method goes here)

Ultimately, I don't think the author has done his homework here because he doesn't address elements of photographic composition beyond "fill the frame" even to dismiss them. I also disagree with his claim that "nowadays we’re surrounded by rigid landscape screens". Laptop PCs have those, but phones and tablets can be freely rotated and are most commonly used in a portrait orientation. Rotating mounts for desktop displays are very common, though it's rare I see anyone else's in anything but landscape.