Ignoratio elenchi is the closest thing I could find.
It is the act of using an irrelevant conclusion to answer an argument. The argument may or may not be logical, but is still irrelevant. In other words, answering the question in the way you wish it had been asked.
The example given: You are asked: if x is illegal?
Instead of yes or no, you answer:
It ought to be legal because …
This is Ignoratio elenchi.
I believe you can extend out the definition to be an intentional dodging of the question.
See also the Red Herring, and the Straw Man Argument.
Update on further reading Red Herring may be a better fit. If used in an argument a Red Herring is an ultimately meaningless answer. It can be intentional or unintentional in nature. But, the purpose is to divert away from the argument.
The origin of the term is supposedly the use of a strong smelling fish to divert hounds that are following a scent.
I believe the answer given by the politician is a red herring in that sense. He has given an answer that diverts away from the question he was asked, but might not seem to have been an evasion on theits surface.