sounds like an encoder with turn-buttons to me. maybe with 2 way speed like on some video-recorders. where you can rewind, fast rewind (turning left) or forward, fast forward (turning right).
It seems that the control in question is from a broken Pro-DJ CD/karioki thing. (Soundlab G064E8).
There are also a couple of sweet blue backlit LCD displays which seem to be intended for track position, pause, FF,REW, speed, etc etc. Pity about these not being a couple of lines of text.
The controller chip also encodes up to 30 keys, and outputs data in serial form. What a shame so much technology is wasted.