Op-Amp comparator or amplifier?
Is the op-amp being used as a comparator, or as an amplifier, or
  something else entirely?


It's being used as a linear amplifier I reckon and if you showed more of the circuit I think you'd find that the top of R5 goes to a positive power (or reference) rail. That positive power rail will dictate what the negative output voltage will be from the LM337.

Regulation occurs when the op-amp's inputs are equal and, because pin 3 is tied to 0V, when pin 2 attains 0V, the LM337 will be regulating.

So if the voltage at the top of R5 is +3.7 volts (pick any number really), the LM337 will output -3.7 volts.