The article doesn't emphasize this quite right.
The key insight of Discordianism is that all of human society is "fake". If you can kick it, it's real; if you can't kick it, it's exactly as real as Eris is -- which is to say, the way people behave is in accordance with the way that they truly believe.
The first level of Discordianism is to think that Discordianism is a joke.
The second level is to realize that it's true.
The third level is to realize that it's a joke that teaches you that everything that exists in and shared between minds has the same ontological basis: Discordia, Islam, Christianity, the US Federal Reserve System, Google -- they all exist because people believe that they exist and behave in ways that indicate that belief.