Double points come in sets of 4 or 5, one is left empty to knit the new sts onto, the rest just hold the needles. You're still just knitting with 2 needles at a time and the others are stitch holders. Look at the dpn video
, though you may have too many stitches to fit onto a set, and would have to do a short circular (until the decreases, then you need dpns or a long circ or 2 of them) or use a longer circular and magic loop. There's videos for 2 circs and magic loop on the same page as the dpns.
If you knit it flat, you'd have to reverse the sts on the even rows, though it looks like a simple rib pattern, so that's not as difficult.