What is the purpose of the choke in this circuit?
Pretty sure that is there to limit the current into a largely discharged battery. 

Basically it adds reactance in series with the (almost) voltage source that is the transformer so as to ensure the current does not rise to silly levels if the battery is very flat. 

Another approach to the same thing that you also see in battery chargers is a transformer designed with a magnetic shunt thereby raising the leakage inductance (to largely the same effect).

Somewhat crude, not great for the power factor, but cheap and VERY robust and reliable.