I think the slide on page 16 is wrong; the inverse square law comes into play when light is unconstrained and spreads out in all directions. Losses that come from impurities in the glass and so forth attenuate differently.

For instance, if you're looking at light intensity from a lightbulb, every time you double the distance you get 1/4th the intensity, or that comes out to about a 6 decibel loss.

If you're shining a light through an optical cable, it might lose half it's intensity every time it goes, say, 10km (I don't know what the number is for proper high-quality single-mode fiber, so we'll just go with 10km). So, your loss is about 3 decibels per 10km.

Over short distances, the small fixed loss of the cable isn't significant, but over very long distances, the 3 decibels per 10 kilometer loss adds up a lot faster than 6 decibels every time you double the distance.

I'd say it's unclear rather than wrong, and what you say is perfectly correct.

Decibels are useful when dealing with exponential decay, meaning that the output of a process is always proportional to its input. An inverse square law is an example of this more general case, so I think the author is just holding it up as an example, rather than saying it applies to fibres. Other examples are inverse (which holds for fibres as you point out), or any other choice of exponent.