In regards to pages 110-113, he only has 465 engagements from which to draw data, of which the overwhelming majority must involve rifles, not smoothbore muskets, as those were the more common weapon during the war to the best of my knowledge. That's not a huge sample size, particularly on the musket side, and I'm not thouroughly convinced by it. Furthermore the man has an agenda (his thesis) and given that "wins" and "losses" are kind of abstract concepts he's tallying himself, I can certainly envision him massaging the data a bit. I'd like to see an independent party review the data. Additionally I am not convinced that the rifle did not have an impact even in battles it did not participate in, as your opponent is not always aware of what armament you are using, and prudence dictates you should assume your opponent has rifles and act accordingly. Furthermore he admits he did find a statistical advantage to the rifle, which he dismisses as insignificant.
EDIT: Then there's the issue that I could imagine that what's happening is that both sides used smoothbore muskets early in the war, and rifles late. If that's the case I would expect him to find what he found. Afterall, if both sides have rifles or both sides have smoothbore muskets no advantage is conferred.