The wood is just for the door frame so they have a place to screw in the hardware and nail in the casing.
They are inside the C channel on top. Maybe the picture is not clear on that.
I agree on the NM, no matter how they hide it. The strange thing is the tray cable would be legit. "In a raceway" is one of the accepted uses in 336.10. I am just not sure how they would have to continue on once they got inside. I suppose they might terminate the NM in the disconnect on the wall. That makes is sort of legal. It is about like feeding the jelly jar next to the door or a surface mounted FS receptacle box outside.
My bet, they strip the jacket and pull it through the Carflex, pretending it is THWN.
