I thought the DH rule allowed a designated hitter to replace a pitcher at bat but it didn't mandate that a pitcher couldn't hit. Therefore as a pitcher Ohtani could hit for himself but then serve as the DH for the pitchers replacing him on the mound.
My underlying problem though is that I hate the DH business in the first place because it flies in the face of the underlying principle of the game, i.e. the nine men playing in the field come to bat in turn.