I agree he could have made a much simpler version to get the point across.
+1
I spent a few years developing auto routing algorithms. One simple test case we often used is this one:

Conventional one-layer-at-the time greedy algorithms had difficulty finding the wire length wise optimal solution (above). For example, they ended up with something like the one below, and if A, E, D, F were on the routing boundary, they could not find a planar solution at all (e.g. if you make a greedy route of A-B and C-D, you have no clearance to route E-F between B and C).

Probably not the most intuitive example of bad auto routing but the shirt could have something simple along these lines.
BTW, I love the eagle auto router. I route manually the critical nets and let it does the rest of the work and when lazy I don't even clean up for aesthetic.