Even in the original Newcomb’s problem there is presumably some causal pathway from your brain to your decision. Otherwise Omega wouldn’t have a way to predict what you are going to do. And there is no difference here between “your brain” and the “gene” in the two versions.
In neither case does Omega cause your decision, your brain causes it in both cases.
Re: the edit. Two boxing is strictly better from a causal decision theorist point of view, but that is the same here and in Newcomb.
But from a sensible point of view, rather than the causal theorist point of view, one boxing is better, because you get the million, both here and in the original Newcomb, just as in the AI case I posted in another comment.