I think it's like this: "The end of the world" is not an event, it's a process. That process is just beginning. We're nowhere near "the end of the end".
Yeah, thanks. The article is about a book called "The End Of The World Is Just The Beginning", the missing "the" turns the meaning of the book title on its head, from an optimistic sounding "this is just the beginning" to a fatalistic "the end of the world is beginning".
At least, that's what I think it's trying to say.