Roger Caillois (1961) classifies games/play into four classes, being: competition (also called agon); chance (alea); mimicry; and vertigo (ilinx). Games are placed in one of these and exist somewhere on a spectrum from paidia to ludos, which are roughly speaking the enjoyment-of-playing (like disguises) and enjoyment-of-rules (like chess) extremes.
Writing, Play and Performance on Internet Relay Chat uses this typology when looking at play on IRC. Caillois' method is intended to be used for just this, a framework for examining play across different cultures. (Found after following notes on Purse Lip Square Jaw).