When the man gets it right, well, he gets it right. And this time he did.
He is correct that there is no way to rescue the common view of free will in a purely natural universe. Quantum determinacy won't help you. Chaos theory won't help you. Coyne (like Bill Provine) is refreshingly forthright here.
Suppose by free will we mean that from the a given initial state at time t0 we can steer the universe to one of two very different states at time t1 by making, freely, choice A or choice B. If that is free will then there is really only one way to explain it: by invoking the supernatural. (Or by invoking the atheistic equivalent, philosophical woo.)
We are not puppets in Calvinism. No sir. But we are puppet-slaves to differential equations in a universe without God.