I believe what the article is referring to by "pull the cable from between the stitches" is a technique of doing small diameter circular knitting called Magic Loop. This technique enables you to use one circular needle instead DPNs. There is a video demonstrating the Magic Loop technique on this site that is excellent.
FYI...there is another technique for small diameter circular knitting where you use two circular needles instead of DPNs. There is also a video on this site demonstrating this technique.
to go to the page that lists the videos for circular knitting. Scroll down until you see the heading Small Diameter Circular Knitting. Listed below that are all the videos you'll need. I'd suggest looking at all the videos and trying all the techniques until you find the one that works best for you. I've done DPNs (never again...it's like holding a handful of porcupines!), magic loop (easy), and two circs (really easy...even when the joints are hurting). Good luck!