I watched the video and read the pattern - the pattern written to follow the cast on method... it sounds like you are to knit a 'toe' up tube sock that will fit a ds. If you knit this as toe up - no seaming needed. The video shows how to cast on, but instead of using double pointed needles, you would use 2 circs. 40 cast on stitches total, 20 on each needle. Since the cast on method already purls a row for you - you only need to knit a few rows then increase - knit into the front and back loops at the beginning and end of each needle - you will then have 22 stitches on each needle - this will help to fit the 'sock' around the bottom/side of the ds. continue knitting rows as described in the video (it actually is knitting in the round, but is hard to visualize because of the toe up/knitting method.) When you get to the end, finish off with the ribbing and then bind off. Weave in your ends and you are all complete.
I'm not sure if it will work on dpns or not - I would think that you would have to have long dpns so stitches wouldn't drop off.
If you wanted to just knit this in the round, cast on 40 stitches, divide over 3 needles, join, knit the ribbing pattern, increase at the end of the ribbing, knit in the round till finished length is reached. Bind off and then sew or kitchner the bottom closed, weave in ends.
I would play around with the cast on method in the video and just practice... I might have to try this myself - my son would love a 'sock' for his ds.