On my Endurapro (PS/2), there was a controller like the one in your second pic secured to the underside of the keyboard assembly to which the pointing stick directly attached. The keyboard's controller (standard 42H' style) was connected to the pointing stick controller as was the PS/2 y-cable. What's interesting about the design of the Unicomp controller is that it acts like a PS/2 keyboard pass through, so it should be trivial (from an electronics perspective) to adapt the pointing stick to work in any keyboard you wish.
If memory serves me correct, the controller in my M13 is like a classic Model M controller except extended at the side. Both the keyboard assembly and trackpoint are directly connected to it. The components on the controller which control the trackpoint are covered in what looked like the lining of a cigarette box.
Your board is neither... It looks like they got an M13 controller, and instead of connecting it to the pointing stick directly, they hooked it up to a controller which 'translated' the pointing stick's signals to ones that the M13 controller could make sense of. I guess this was back in the day when they had large quantities of surplus IBM stock, so this might have cut down on the complexity of the components they had to make themselves at the expense of being rather hackish.