This circuit uses a transformer on a rectified DC voltage, what purpose does this serve?
It's called a fly back transformer. Energy accumulates in the primary during the first period of the switching cycle. In the second period, that accumulated energy gets released to and used by the secondary. It's not used as a conventional transformer and there is more than one way to skin a cat.

Transformers can be used on a dc supply providing that the average voltage applied is zero i.e. the transformer magnetics are allowed to reset or fly back.