Yeah, you are kinda missing something. It shows you how the chord patterns connect up the neck. I personally don't agree with a lot of points the articles author makes, but I may be approaching the CAGED system differently.
Consider an E Major chord. In 1st (open) position you can play the E Major chord with the standard E Major open shape (022100). The next place up the neck that E Major shows up is with a D major open position shape (XX0232) slid up 2 frets (XX2454). After that E Major shows up in the C Major shape (X32010) slid up 4 frets (X76454).
I'm going to pause in the progression up the neck to point out some overlap of notes. You'll notice the E Major shape and the D shape (of the E Major chord) share a note - the E on 2nd fret D string. You'll also notice the D major and C Major shapes of the E Major chord share 3 notes - (XXX454). This "sharing" of notes I find particularly helpful in transitioning from one position to the next.
To continue up the neck, all E Major chords:
A major shape (X02220) - (X79997)
G major shape (320033) - (12 11 9 9 12 12)
E major shape (022100) - (12 14 14 13 12 12)
And the pattern starts over.
Now, why is this useful? I suppose there are a number of different ways to apply the theory buy here's what works for me.
You want to play an Emin7. Well, you could play the 1st position chord (020000). But that's just not quite the sound you're going for, you want to play it higher up the neck. You know Amin7 could be played (X02010). So, using CAGED theory, you know the A major shape (X02220) for an E Major Chord roots on the 7th fret (X79997). You know how to turn an A major into Amin7 so now you can turn that E Major at the 7th fret into an Emin7 (X79787). The ability to use open chord theory anywhere on the neck in any key is my favorite use of CAGED.
The second area I find it benefits me is Chord fragments for comping. Playing the same old open position chords or E and A shape barre chords can get dull. Now you can play 2, 3, or 4 note chords all over the neck in many different shapes. It adds variety and can keep your playing from sounding stale.
Next time you need to play an E Major try some of these neat fragments - all E major when played against an E root):
(XX645X) - based off Cmaj shape
(12 11 9 9 X X) - based off Gmaj shape
(X769XX) - based off hybrid of C and A major shapes
(X X 9 9 9 12) - based off hybrid of A and Gmaj shapes