Yeah, that part is a bit poorly worded. I should probably try to fix it in the guide.
The strips are there so that the foot of the sewing machine can slide along without catching on the insulation. When I tried sewing without the strips, the points on the foot would catch the insulation or the insulation would just be too thick and squishy to fit under the foot, and so it would stretch. What I ended up with was my insulation stretching a good three inches or so because of it. By putting the strips on there, the foot has a smooth surface to press down on, and the insulation isn't stretched. Besides the strips, sewing it is just like sewing anything else. And once you flip the whole thing so the right side faces in, the strips cannot be seen anymore anyways.
Hopefully this helps a bit more with clarifying the purpose of that step.