Actually, Roger Caillois wrote a famous book on the different forms of play [1]. He uses four forms of play to classify games, and the one you are referring to is chance (Alea in his book). Another form of play that applies more accurately to chess is competition (Agon in his book). He also emphases two other key components of fun: playing a role (Mimicry) and physical sensations like in a roller coaster (Ilinx).
