This chain bind off method is the same as binding off using a crochet hook, which is covered in another tutorial. Use the one you're more comfortable with... they are just two different ways to get the same result.
Step 1: Wrap and knit off pegs 1 and 2.
Step 2: Move the loop on peg 2 to peg 1.
Step 3: Knit off peg 1 (bring the bottom loop over the top loop).
Step 4: Move the remaining loop back to the empty peg. This peg is now peg 1.
Step 5: Wrap and knit off (the new) peg 2. (Note: this is where you control the stretchiness of the bound off edge -- the tighter the loop, the less stretch you will have.)
Step 6: Repeat steps 2 - 5 until there is one loop left on the loom.
Step 7: Wrap the peg with the loop on it and knit off. Cut the yarn, leaving a 6" tail. Take the loop off the peg and pull on it until the cut end of the yarn comes through. Continue pulling until the loop is closed snug against the knit fabric.
Tip: to put the braid of the bind off on the wrong side of the knitting, purl the pegs in steps 1 and 5 instead of knitting them.
Note: I learned this method from Isela Phelps' blog, all credit goes to her. I just provided the video.