I'll tell you what I think (operative word is think) the posted circuit is. This circuit looks like and reminds me of a circuit I have worked with, though a decade has passed. I do not think the motor shaft is linked mechanically to the pot. Years ago I worked with AVC (Arc Voltage Control) units. We looked at the actual arc voltage gap and the voltage across that gap. As the weld head traveled around a part with an uneven surface the idea was to keep the distance between the tungsten electrode and the workpiece a constant. The distance between the tungsten electrode and workpiece was a function of the voltage drop across the gap.
Forget the photo cells for a moment. They are a varying voltage. Depending on the light dark relationship, acting as a voltage divider, they output a voltage that is a variable. The reference pot in the circuit, however, is a fixed voltage. The pot is not ganged or mechanically connected to the motor shaft. The first opamp is a buffer. The second opamp is a differential amplifier that will output the difference between the variable from the photo cells and the fixed reference voltage. That difference will drive the motor seeking a null or zero difference. If I set Vref = 6 volts and the output of the LDR divider is 9 volts that delta of 3 volts will drive the motor till the delta is zero volts and the motor stops.
The gain pot in the circuit sets the gain. If the gain is too low the motor response will be sluggish or non existent, if the gain is too high the motor will jitter. The idea is to set the gain for a nice smooth motor response.
I ran a simulation on this that looks like hell for wiring as following a long work week and starting a nice 3 day weekend I am sitting here enjoying a few beers and tired. However, I believe the circuit is using the motor (like driving a rack and pinion gear) as a servo motor. I can clean up the simulation tomorrow and post it if anyone is interested. But that is what I believe you have in that posted circuit.
Ron