Explaining mental stuff in terms of non-mental stuff implies that we are atoms and nothing more, and are under the same laws that govern all physical events, so I am no more free to choose to close my eyes than a photon is free to bounce off a half-mirror.

Under physical laws doesn't mean under deterministic physical laws.

What does vitalism have to do with free will?

Having reduced mental stuff to non-mental stuff (atoms and interactions), the only way to preserve free will is to postulate the existence of some mental fundamental essence which inanimate things don't have,

Who told you that? Naturalustic libertarians reduce free will to specific combinations of physical determinism and indetermimism.