I'm not a lawyer and I don't play one on TV. That being said searching around results in some interesting results. One way to interpret this is that the tax applies to the sale itself, not the act of transportation. Regardless, the taxes go to the tax authorities, the airline does not keep them even if you did not take the flight. So if you are entitled to a refund is one question, but you would have to ask the tax authorities, not the airline, for a refund.
My understanding from a quick look on the internet. Hopefully someone with actual knowledge can jump in.