Understanding a chinese Ringing Choke Converter
The way I would think of this is that the 25uF capacitor and associated 1N4148 diode form an analog of the output voltage on the mains side of the transformer. 

I think there's something wrong with where the zener diode and/or 3.9K resistor goes- it should inhibit the base drive of the BJT to regulate the voltage. 



Edit:- 

The red LED effectively goes on when the voltage across the 91 ohm resistor exceeds about 2V, so presumably when the current flowing into the battery drops enough the primary current pulses drop enough that the red LED goes out. Probably this only works sort of well for a 230VAC input, and not so well, if at all, for 120VAC since it's measuring primary current pulses.