First post from a lurking noob. I'm a 2-spacer as well. I learned the practice when I took typing in junior high school and it carried over into computers since, as the article mentioned, computers used fixed spacing as did those old dot matrix and daisy wheel printers.
What the article didn't mention (unless I missed it) was that those old fashioned lead typesets commonly included two different space pieces (quads): the en quad and the wider em quad. At least some word processors, like Microsoft Word, also use these spaces. En spaces are automatically inserted between words while em spaces go between sentences. However, this isn't universal. For instance, this forum software does not do so.
While the typographer in the article may be technically correct, I prefer the wider spacing that two en spaces provide. It improves readability to my eye. But since I'm an administrative professional, I guess I should change my ways...at least when using Word. That way I can be technically and "inarguably" correct while having my slightly wider em space cake and eat it, too.
Side note: Capital letters in those old tin type sets were commonly kept in a separate tray (called a "case") in a drawer or shelf located above the other letters, hence, "upper case" and "lower case" letters.