To me I would have thought a voltage regulator and transistors would have been all that was needed for the controls.
Chad, when used with a motor, a regulator is acting like a power resistor. That's just wasting power. Also, the regulator needs 1-2V of drop to work, which can be limiting.
My guess is you are close with your original idea. The op-amp is a control circuit that maintains a constant current running to the motor. This would make it a little more stable as the battery's voltage changes and would have allowed some control over how fast the motor spins.