Those directions are for felting, which will certainly make a knitted object smaller but, as you already guessed, only works on animal fibers such as wool. You may not melt the acrylic by giving it the hot-cold-hot treatment but you won't shrink it either.
You do have some options, though. (1) Get a spool of elastic thread and sew several rows of it through the inside bottom edge of the hat. Pull up the elastic until it's the right size for the young man's head and tie it off. The hat will be nice and snug at the bottom edges. The top will still be large but at least the hat won't fall off. This trick also works for loose necklines and cuffs. (2) Frog it and start over, watching your gauge to be sure the new hat isn't too big. Try smaller needles if you can't get the gauge. (3) Give the hat to an adult male with a large head, make a smaller one for the boy, and act as though that's what you had planned all along.