They haven't exactly been clear about the laws in the show
Not in the show but its pretty clear in the books. The Targs even fought a whole civil war when one highborn bastard was chosen by the king over his true heir. I am talking about Daemon Blackfyre for those who read the World of Ice and Fire.
He has either received a hit to the spine (but that would be awfully convenient lucky hit) or there was some kind of a poison (which we got no indication of). Either way it wasn't the strongest part of the episode
Its wasnt too unlikely. I assumed he was stabbed in the liver. The positioning looked correct. That will result in a very fast death compared to a stab in the stomach.
Theres a scene in the movie Gangs of New York where Daniel Day Lewis was teaching Leo Caprio how to kill a man quickly. One ofthe stabs was to the liver. That came to mind when I saw this scene.