The tutorial is about thinking in terms of tufts and layers of fur rather than single strands. Although some furry animals, especially young ones, are nondescript fuzzballs, most have distinct tufts or even layers of tufts that their fur clumps into. For example,
check out the lines on the neck and chest of this bear, and
on the abdomen of this one. By stylising these clumps, you can get fur that reads well, communicates the form, and looks awesome. Although normally I recommend looking at the real thing over artists' renditions, in this case other art might help you see this clumping more clearly, since some animal artists have it down to a science.
Here, for example, check out how the artist has used both layers and tufts on the back of the front legs, while keeping some parts smooth, which gives a sense of varying, flowing fur.
Some(1)
more(2)
inspiration(3). These are all paintings so they have room to add more detail, but the basic idea of clumping carries over to pixel art fairly well.
You should check out
this thread here on Pixelation, it deals with pixelling fur in a couple of different ways, at a size comparable to yours. Clumping is very helpful to keep in mind when deciding where to place the shadows/texture that creates the fur.