The first section is used for sprite animations.
Essentially you have a sequence of textures that loop.
You add all of the textures that you want to the model.
Then in the material layer that draws the eye, set the texture to animated, and add keyframes that use the relevant textures.
You can inspect the Water Elemental model in Magos or whichever application to see how it works.
The Water Elemental also has the second type of texture animations, which is used to animate texture coordinates with translation/rotation/scaling.
Technically you can use this for a sprite animation as well using a texture atlas, much like how particle emitters work.
That being said, it's generally used for surfaces that "move", which is why the tutorial calls it so.
For example think of a lava surface where the lava flows in a certain direction.
Another example is the Volcano model, which uses scaling texture coordinates to have rings that move from the center outwards.
I think in this case sprite animations make more sense, but I am no artist, maybe possible to get a decent result with scaling texture coordinates that scale inwards...?