The signal from Q3 is fed to two 50:1 dividers then from the dividers to the Q4 and Q5 buffer amplifiers.
The two halves are functionally identical and should produce near identical signals at their collectors, so little or no voltage across the meter rectifier.
When a capacitor is connected to the test terminals, the ration of the 10:1 divider is changed as the capacitor is in parallel with the 3 Ohm resistor.
So, the signal through Q4 is reduced to some extent; the lower the ESR, the more the signal is reduced.
Any reduction unbalances the signal across the meter rectifier and gives a reading proportional to the imbalance. I'd assume the meter is calibrated via the pot in series with it to read full scale with the test terminals shorted (0 Ohms) and higher ESR values give proportionally less meter deflection.
Just like an analog multimeter; 0 is full scale.