It's simpler than it looks! The op-amp (741 or if you're going to build one today, use TL 071) is a simple non-inverting amplifier. The gain is set by the ratio of the feedback resistor to the resistor from the inverting input to ground (DC blocked by a capacitor). The 3080 is used as a variable gain amplifier. The gain of the amp is controlled by the current fed to pin 5 from the transistor rectifier circuit. The 3080 bypasses the feedback resistor around the 741, so the gain of the 741 can be changed by increasing the gain of the 3080. The whole shebang works as a controlled-gain amplifier, the gain of which is set by the current developed into the 3080 from the transistor rectifier....
The Dynacomp (and Ross, and lots of others) use the 3080 on its own as a gain control stage. The 3080 is a pretty poor amplifier (it's noisy and has lots of distortion) so EH used this clever feedback-controlled amplifier to mitigate the poor performance of the 3080 and the 741 - as the 3080 gain increases, there's more and more negative feedback around the 741, so distortion is reduced, noise is reduced, and frequency response is improved!
This kind of gain cell is quite effective, and has low noise and distortion, but has a few problems - it can't reduce the gain of the op-amp over a huge range (18 dB is the usual practical limit), it can introduce noise due to the DC level changes in the circuit, and it's more complicated than a simple VCA stage.
It's interesting to note that this type of gain cell was also used in the Morley compressor pedal.