This may be a bit off topic, but I don't think that explanation is quite right. She wrote:
But her first example is one where she cropped but didn't change distance to the subject. She later focuses on relative distances, but why do relative distances matter?
The key is angle of view, not distance per se. One consequence of angle of view is that the wider the AOV, the closer you have to stand to a subject to obtain a given size relative to the frame and, as she points out, the greater the relative distance behind the subject compared with the distance in front. But it's because of AOV that this matters, I think.
Start with this diagram of a narrow AOV:
I drew this with distances in cm, which isn't a good example for most photography, but the choice of units doesn't matter. In this diagram, I have positioned the camera so that a 4-unit subject completely fills the frame. I then drew a line indicating 10 units farther away. Given this angle of view, 10 units further away captures a length of 7.5 units.
Now look at this wider-angle perspective:
As the article noted, I had to move closer to fill the frame with the 4.0 unit object. That's not the key. The key is what happens 10 units farther away. Now it takes 13.2 units to fill the frame at that distance, and the 7.5-unit object that filled the frame with the narrow AOV (shown in this picture by a thick black line) now fills only 57% of the vertical distance in the frame.
In other words, with the wider-angle lens, the more distant object looks smaller. This is where relative distance matters: we need something to anchor our impression of the size of the things farther back, and the foreground subject does that. We we process smaller, relative to the near object, as a cue for greater distance. Going the other direction, tighten the AOV, and the distant object looks larger relative to the frame. We process that as a cue for shorter distance. Hence, "compression."
These diagrams also show why a longer lens will produce greater background blur, independent of DOF. Given a fixed distance from the lens, the longer the focal length, the smaller the object that is stretched to fill the frame--hence, more blur.