Millers number The renowned psychologist George Miller is most famous for discovering a certain limit to the human short term memory. This limit has to do with the number of information bits that a person can remember at any one time, he called it the Magic number 7 +- 2. This in itself has absolutely nothing to do with design, just as the article on UXmyths has detailed.
Short term memory and decision making To think about something we need to hold the different thoughts or parts of thoughts in our minds. This is especially important in decision making where it is not to your conscious advantage to forget parts of the decision. Since this is limited to 7+-2 we can never remember more parts of any choice. But what about ideas? What about bits of information that are really just the sums of huge amounts of other information? To handle things like this we use chunking.
Chunking? Chunking is the process where we categorize information that fit together, for any satisfactory reason, into one bit of information. For example a car is seen as a car not "a metal body with chair in that sits on four wheel rotated by an engine". For the best explanation of chunking vie seen to date check out visual chunking and the law of Prägnanz. LINK
Why does this support Millers number in design? Millers number sets a upper limit to chunks before they become noise. So while it is quite useful to have a menu with more than 7+-2 choices it would be really frustrating and hard to remember if there were more areas of interest or chunks of information on any one page.
So millers number is excellent in design, UXmyths is dealing with the simplified use of Millers number which leads to results that are just plain wrong.
In a sentence: Make sure you understand complicated psychological theories before you apply them to design.