I am a believer in Free-Will, but do not think this argument proves Free-Will. My objections are as follows:

1. If it is true that determinism is self defeating for the intuitive reasons suggested, this does not necessarily mean determinism is false. It just means that IF determinism is true then there is no valid argument for anything including determinism and everything else.
2. I do not think it obvious if determinism and free will are a real dichotomy, and I do not think every one agrees with the particular meaning of either term but understand them somewhat differently. For example for my own working definition of Free-Will and Determinism they are not exclusive.