The two orbital arrays in Figure 3 are just examples and do not correspond to real systems. In inspecting the Möbius one on the left, plus-minus overlaps are seen between orbital pairs 2-3, 3-4, 4-5, 5-6 and 6-1, corresponding to an odd number 5 as required by a Möbius system. Inspection of the Hückel one on the right, plus-minus overlaps are seen between orbital pairs 2-3, 3-4, 4-5, and 6-1, corresponding to an even number 4 as required by a Hückel system.
The plus-minus orientation of each orbital is arbitrary since these are just basis set orbitals and do not correspond to any molecular orbital. If any orbital were to change signs, two plus-minus overlaps are either removed or added and the parity (evenness or oddness) is not changed. One choice of signs leads to zero plus-minus overlaps for the Hückel array on the right.