"so the premise of the paper that there is a valuation function v(s), where s is the board position, that determines game outcome is incorrect" No, it isn't, a

"so the premise of the paper that there is a valuation function v(s), where s is the board position, that determines game outcome is incorrect" No, it isn't, any more than the claim that there's a position evaluation for chess is incorrect because of castling and capture en passant. A "position" isn't just where the pieces are on the board, but includes all relevant state information.