The 4066 is a phase lock loop IC.
The frequency of it's internal oscillator is controlled by the voltage at "VCO In" (plus the external components to set the range).
That normally tries to track the input frequency, by comparing the oscillator to the input in a phase comparator.
The output of that connects to the VCO in via a resistor.
The audio signal is also applied to VCO in while the relay is closed, which nudges the oscillator frequency up and down with the audio waveform, with the phase comparator continuously trying to match the input.
To me it does not look right; I'd expect some other components - a capacitor at least - in line with the relay. Without that, P1 is being switched in parallel with the lower half of P3, changing the DC bias as the relay opens and closes.
And turning the audio gain P1 down would effectively disable the VCO control from the phase comparator, locking it at 0V.