(Wait, if God kills you, isn't that still extrajudicial? God isn't working for the government.)

Not really. Divine judgement qualifies for two out of three definitions of judicial right of the bat and then we have to consider that for religious purposes everyone is considered to either belong to a Theocracy under God or be a heathen enemy of the state. On top of that God's scriptures dedicate much of their content to setting up a legal system, with a book outright dedicated to "Judges". If it wasn't for the fact that God just doesn't exist I think it'd be fair to say that he claimed precedence on "Judicial" a long time back and human states just borrow the concept.