A car battery charger is 12v dc, so I don't know why someone would use it (though being a universal motor, it can run on DC). Sounds to me like someone looking to do a clever hack, given the price of hobby transformers these days I don't know why anyone would do it.
Interesting that he decided to put the speed control on the A/C input (basically a variac), rather than a rheostat on the 12 v dc output. I can't see how using the A/C input voltage control would work any better at low speed control, the voltage is stepped down and rectified and the a/c input voltage controlled variac isn't likely to be all that fine in terms of voltage 'steps', wouldn't be different than a rheostat would be *shrug*.
