Well... it looks like you have a bunch of tactile switchs from the buttons that were on of the stick. If I recall correctly, there was a "hat" style thumbswitch on those joysticks as well, which would detect left, right, up, down, and diagonals (probably by combining left & up, left & down, right & up, right & down). I'm going to guess there are a few transistors on there as well. Looks like there is also an optical encoder for a wheel of some sort. Need to look at the pictures some more...
UPDATE: Scratch that... no rotary encoder. I hadn't yet looked at the top-down picture and see what I thought was the encoder was just the side of one of the hat switches. If I read your diagram correctly and look at the pictures, there are 8 buttons but only 6 wires. My guess is that like they are multiplexing the input. Meaning... they are using the transistors to switch which buttons they want to "read". In order words they can only read some of the buttons at a time, and they use the transitors to switch which buttons they are reading.
I'm thinking that the blue, orange, yellow, and green wires are where you read the inputs, and you switch which inputs you want to read by applying voltage to either the red wire or the brown wire. I think the red wire will let you read inputs 1,2,3,4 off the input wires and the brown wire will let you read inputs 5,6,7,8 off the same input wires.