Maybe not. If you use different yarn and smaller needles you might be able to follow the pattern for the smallest size and it would fit your son. He's 12 right? About the size of a small woman maybe.
What needles and yarn do you want to use and how many sts/per inch do you get? How big around do you need to make it? That's all the math you need to do - figure out how many stitches you need to get it around him and then look for a CO number about the same. Then follow the pattern for that size, keeping in mind you might not make it as long as for an adult.
But if you want to go ahead with the other pattern, that's cool too.