What is the role of magic? What is the supernatural in this tale?

I believe the magic largely comes from the Green Knight himself. As the Green Knight, he represents an otherworldly, natural force intruding into the refined circle of Camelot. His green color, enormous size, and apparent immortality indicate his otherworldliness; he seems allied with Nature in all its furious, regenerative grandeur. Nobody had ever seen a figure quite like him before: especially a figure that could pick up his severed head and close the deal on the bet!

All those standing there gazed, and warily crept closer,
Bursting with wonder to see what he would do;
For many marvels they had known, but such a one never;
So the folk there judged it phantasm or magic.
For this reason many noble knights feared to answer:
And stunned by his words they sat there stock-still,
While dead silence spread throughout the rich hall
As though everyone fell asleep, so was their talk stilled
at a word.