That seems to be milking the explanation for all it's worth!

The short answer being that if something is radiating out 3-dimensinally in all directions, then at a given distance, r, that thing (light/whatever) is being spread out over an area equal to the surface area of a sphere of that radius, which is 4 x pi x r^2, i.e. the intensity is inversely proportional to the square of the distance (r^2).