That transparent wheel with the markings is the super high resolution encoder. The black thing covering the wheel is an IR detector, basically counting the black tick marks when the IR light is blocked.
Unfortunately the circuit board wont be hackable, and is useless.
I am guessing you want to hack the printer to do high position stuff, but with your own controller right? All you do is plug the IR sensor signal line into a digital output of your controller. Use interrupts, timers, and a feedback PID control system. You then have the microcontroller control a motor driver to actuate the DC motor. Its fairly trivial in terms of work required, but implementing a control system for your first time takes a little while to understand. But definitely a simple project so I dont think you will have that much trouble.
If you plan to scrap the printer, these are usefull things I see that you should save: