Here is the stereo amp in question:
http://electronics123.net/amazon/datasheet/k115v2.pdf

How does the single potentiometer control the volume for both left and right signals? Is that a special potentiometer that is like two pots built in to one, and are electrically separated?

 

Yes, its like you have two pots in one package which can be adjusted by the same knob as to have almost the same output voltage.

 

Pot1 is a dual ganged log pot.

It's two pots linked together on a single shaft.