Uuuuuuuhhhhhhhhggggggghhhhhhhhhh, they used that voltage doubler circuit (forgot its name) in a modified form to supply the 7812. It works, but you can't draw that much power. Now that I think of it, 9V * 1.41 = 12,69V, which is too low for a 7812 to work and quite high for a 7805. Substract 0.6 Volts forward voltage drop for each diode in the way and you get even lower.
I'd say let's NEVER EVER replicate the stock PS design and use some better stuff instead!