capacitative battery charger
The capacitive supply description is correct. This is a capacitive dropping supply. When connected to AC, capacitors look like resistors. The impedance (similar to resistance) depends on the size of the capacitor and the frequency of the AC source. This "resistor" is used to control the current by dropping some voltage across it. In this case, a 50MFD capacitor at 60Hz is about 53 ohms of impedance. The reason they use a capacitor is it's more efficient. The capacitor will dissipate far less heat than the equivalent 53 ohm resistor. 

As far as overcharging, there's not a whole lot you can do. This is not meant to be a battery charger outright. This circuit exposes the battery to high voltage pulses to desulfate the plates, not to charge the battery. This is why there is a timer built in. A battery will only take so much abuse and the timer automatically limits that abuse. 

If you want to charge batteries then buy a dedicated battery charger. If you want to desulfate batteries then you could reduce the size of the capacitor to reduce the current.