Yeah, the kraft paper is there to keep air from blowing through the wall. It's a natural version of the plastic used on normal construction. Insulation doesn't work well if the air is being pushed by wind, or the
stack effect, through the wall. It just takes the heat out with it.
So the 3/8ths inch boards are functionally to hold the paper and insulation in place and protect them. It also gives you something solid to bump into with your shoulders or to mount stuff to. And it's pretty. Its insulation properties are negligible compared to the rockwool behind it.