The following line:
Round 3: K all stitches on both needles (no decreases).
Should read:
Round 3: K all stitches on both needles (no increases).
This should be the last picture in the article between DPN step #9 and step #10.
It illustrates step #10, knitting from the second cast-on needle to the the third and fourth needles.
Click on the picture to see a larger version.