In Gawain and Green Knight, the Green Knight is a rather enigmatic. He walks in and challenges king Arthur to a game and that game is to cut off their heads. Green Knights head would cut off his first and a few years later the Green Knight will come and cut off king Arthur's head. Everybody thought this was a joke, but it was quickly obvious that he was serious. Arthur was about to accept but Gawain accepted in his place and he decapitated the Green Knight. The Green Knight picks up his head and just leaves casually.
Why would he treat his life as a game like this. Because no matter what Gawain did to him, he would not die so if death is not something to fear then it will eventually become a game. If I was immortal, I would treat it like a game. Like trying to die in the stupidest way posable. The Green Knight must have a similar mindset.