As I understand an urban aera is ONE city. Like Beijing or Guangzhou which contains parts of other villages in it. But its called Beijing. The Ruhr is a river in Germany and the cities on this river are called Ruhr Aera. Again, there is no single city in Germany which is called "The Ruhr".
The source defines the Ruhr as a whole urban area with no central city, while Beijing and Guangzhou are the central cities of their areas. And considering that the source is a German site (where the Ruhr is), well, they should know more if it counts this way.
But I do not understand why this is called in english "The Ruhr". The Ruhr is a river as I stated before. In german its called Ruhrgebiet (Ruhrarea). I never heard somebody say "Die (The) Ruhr" when talking about the Ruhrgebiet and I'm from Germany, so I know more if it counts this way.