Types of games??

Firstly, the paidea/ludus bit. Kind of strange this, since all games are, by their nature, played for pleasure. If Ludens describes a game as ' a subset of play' (Salem and Zimmerman, 2004: 71-83), and play as 'an activity with no material interest'(cited in Salem and Zimmerman, 2004: 75), then what about sport, music and gambling, to name three activities which are pleasurable, but have a definite material interest; professional sports, gambling (obvious), and the music/arts industry. Then there is the bit about rules, which, according to Ludens, are fixed; so a kickaround in the park could not be described as play - no rules - but is a 'free activity standing quite conciously outside ordinary life' (cited in Salem and Zimmerman, 2004: 75).
So I am not sure that paidea/ludus, as types of game, mean very much.
As far as videogames are concerned, the only type of videogame that could be described as Ludus would be online gambling. Any other genre could only be described a paidea. (Ok, in some countries there are competitions with monetary prizes for winning a game of, say Unreal Tournament but these are not the norm).

Then there is the Agon/Alea/llinx/Mimicry bit. Again the lines are blurred. A Mimicry kind of game, such as RollerCoaster Tycoon or SimCity, could be said to be Agon if there is a particular
population or monetary target to be met. Some of the flight sims could be labelled the same way,
since targets could be assigned to be destroyed in order for the game to progress. X-Wing (LucasArts) is such an example. Actually, X-Wing, like a lot of other fighter pilot sims, combine all of the attributes, movement of the controls, and chance being the random nature of the enemies. (That last part depends on the age of the game, since most enemies in early games were scripted in their behaviour).
I am curious about these labels, though. For instance, how do you define God games, or strategy games. In some cases, such as the Tycoon series, they could be seen as a type of mimicry, but what about Civilisation (Firaxis), Empire Earth (Sierra) or Age of Empires (Microsoft). All of these examples have elements of all the types so there seems little point in labelling them at all.
And maybe that's the point. Should games be classed according to type, or as seems to be more popular, genre. I mean a shoot'em like Unreal Tournament has all of the types, but is still just that. A shoot'em.