That's called a synchronous vibrator. A second set of points does the job of rectifying the stepped-up voltage coming out of the transformer.
A radio using a synchronous viber is sensitive to supply voltage polarity. That is, if the radio is negative ground and you reverse the input polarity, the stepped-up voltage will also have reverse polarity. It'll be putting "B-minus" voltage on the filter caps instead of "B plus" voltage.
