The concept here is not a charge pump, but rather an isolated, current limited supply to charge each cell as if it were on its own - like using multiple single cell chargers. There is a resemblence to a charge pump here though, I must admit
The output of a PC power supply transformer wont do what you think - they are usually driven half-bridge, and use a common centre tap for ground/neg and a half-bridge diode (two diodes back to back) to feed the + output (and caps etc). Each side produces pulsed DC rather than the AC you would expect from an iron core transformer being driven from AC (or full bridge). This saves on having to use full bridge commutation on the primary and full bridge rectification on the secondary - the main reason for the diodes are to stop rogue flyback pulses getting through to the output, not that there is nicely balanced AC output.
PC power supplies are a marvel of cheap construction methods








