Each one is the full 4 quadrant compass as seen by each of the quadrants.
Top-left is authleft perceiving all politics as the imposition of the power of one class over another (making libleft and libright meaningless terms)
Top-right is authright perceiving all politics as relating back to national identity (making libleft and libright meaningless terms)
Bottom-left is libleft perceiving no difference between domination by state or private institutions (making the left/right distinction in the authoritarian/libertarianism axis meaningless)
Bottom-right is libright perceiving libertarianism as a right-wing phenomenon (making libleft nonexistent).
I'm not following why the given Auth-right position would mean that the libertarian side of the compass does not exist. I feel like what they actually would say is something like "Doesn't exist because some people just can't be trusted to ever become good people."
Many authoritarian types assert that everyone is as authoritarian as them, just with different social and political values which modify how that imposition of authority presents itself.