This split stitch appears to be the designer's own invention (as far as I can tell). Anyway...
You need to hold TWO strands of yarn together (side-by-side) as you work. When you CO this way each stitch will have TWO loops (one from each strand). Then as you work the piece you will be working these loops in various ways, rather than working each stitch.
Ex. When knitting, the 1st stitch has TWO loops. You knit the first loop. Then you knit the second loop together with the next 1st loop (akin to a K2tog). Once at the end you have one 2nd loop and one full stitch remaining, which are all knitted together.
Ex. When purling, you purl the 1st loop of the 1st stitch. Then you purl the 2nd loop together with the 1st loop of the next stitch (akin to P2tog). Once at the end you have one 2nd loop and one whole stitch, which get purled together.
The directions are wordy but oce you get started it will be easier to see.