In the end, the Princess lost 2 pieces while the Chancellor lost 7 pieces. Not sure how many moves that would take, but it's more then the two we are shown.
@jipowap
Not only are we not shown the board state at any point, but we are also deprived of what pieces each player captures, only the number.
I'm guessing the mangaka wasn't very knowledgeable about shogi, and had no desire to research it either.
Not that I really blame them. I can only imagine the lynchmob that would form in the comments section if he botched a play... the audience do be assholes like that at times xD