Also, I can located which one of the 4 pins are X1, X2, 5V and Ground, then could I simply solder wires from these four pins right to the underside of my USB mouse PCB somehow? Will the USB mouse be able to decode the signals the Pole Position PCB sends?
Assuming Aceldamor had his figured right, it should be, from left to right, X1 +5v GND X2 (in the following picture, the 4 solder points at the top of the circuit board):

I think it is correct, judging by the fact that:
1) The +5v goes directly to the resistor
2) The other side of that resistor goes to one of the optics
3) The other side of that optic is the Ground
This logic holds for my Star Trek spinner and the Atari 720 Optics. Assuming that the same logic holds for the Pole Position card, you should be all set.
Luckily yours doesn't look so complicated as the one that Eightbit has, so you shouldn't have to take the board apart.
Once you think you know which pins are X1, X2, +5v, and Ground, I describe how I did a similar hack (720 Optics->USB mouse). Also, there are a few links to some other pages that describe mouse hacks, that I used when I did mine. Check out the following page:
http://www.jstookey.com/arcade/720/720-arcadejoy.php