Have a look on the schematic of the Hameg HM8030 and you will understand how it works.
Frequency is proportional to voltage (VCO of the function generator), then, if you displays this voltage (with adequate voltage divisor), you are displaying the frequency.
It's not necessary to convert output of the VCO (frequency) to an analog voltage, you already have this analog signal.
I agree, that's not a high precision reading, as you are not really measuring the frequency, but that's enough....those 8000 series plug-in's are not intended for profissional use and linearity of the VCO is quite nice.
You could also use the same ADC circuit to display the output voltage. (with a switch frequency/RMS output voltage and an AD8436)
NB: AD8436 is limited at 800Khz.