What is this check/checkmate rule in Shogi?
You were allowed to move to the green spot because the rook wasn't promoted yet, it would only be after it moves again. Otherwise, dropping would be too powerful. See the drop rules:


  ... nor does dropping within the promotion zone result in immediate promotion. Capture and/or promotion may occur normally, however, on subsequent moves of the piece.


The computer decided it would be best to promote the rook on the next move, but for that it had to move even though it was protected on the square where it was dropped.