See, I disagree with what they are saying though. They compare 2 paragraphs, one with double spacing and one without and then say that the one with double spacing has too much white space. Personally to me, the one without looks more like a wall of text and is less readable.
Plus he filled his paragraph with unnaturally short sentences to make it look like there was too much blank space. Of course it will look like that if you're double spacing after every 3rd word, but I'm going to guess that most people write 3 words sentences a whole lot less often than the 40% of the time that he did in his example.