Remodeling a pre-1920's home with planks on the interior walls
Most likely it is shiplap. We just remodeled our kitchen in our 1935 house and underneath the drywall and paperboard, we had something similar. Actually the order was: shiplap, cheesecloth, several layers of wallpaper, then either paperboard (lower half) or drywall (upper half).

As far as whether or not it is structural, we went with the assumption that it was. I'm sure the vertical spacing of the studs in approach does not meet current building standards. However, I am not an architect either. At the very least, having it behind the drywall makes it incredibly easy to hang the drywall and anything else for that matter.