You may be right about the chin cup im still tryin to figure that piece out. But the main face piece appears to be simply decorative. On the site you listed one of the side profiles shows the cuts in the leather.
They frayed the edges and turned them over to give it a thicker appearance and you can see those cuts on the side, you can also see the cut along the jaw line and see it end at the edge before the leather is bent over. That makes me think they are only decorative and so are the rivets.
But maybe im seein things wrong this is my first time working with leather, got any tips for me man, sounds like youve done this before.