It's all a bit rubbish really, we have had at least three changes in the succession since the 15thC, so this is all pretty academic, the Queen is descended from William I through several different lines most of which completely bypass Edward IV whose line died out with Elizabeth I IIRC. As the article says, who sits on the throne is governed by the Bill of Rights and The Act of Succession and the general gist of that says that if the Archbishop drops the Crown on your head, you are annointed and say the various oaths WITHOUT anybody complaining at the time then you are the Sovereign.
Blimey..when I first saw "14th Earl of Loudoun" I thought made-up name! However it is all kosher and he is a legitimate descendant of the Duke of Clarence - famously drowned in a butt of Malmesy. It is a shame he is a republican because this would be such a money-spinning epic challenge...and I'm not even a genealogist or lawyer!
May be he can be the king of Australia. Then it kill 2 birds with one stone. (the Auss prefer have their own head of state while they don't like him/her to be a politican and This man got a good claim to a throne)