Some thoughts following on from my last post.
I should point out that my definition of games is clearly not a complete definition. Something which has no purpose outside itself might well be considered something worthwhile in its own right. Consider: "living a valuable and worthwhile life". It seems odd to class that together with tiddlywinks in the category of 'games'. (It may be that life is a game, or is ultimately meaningless, but I would hope that we can find a way of distinguishing games from the rest of life while remaining agnostic on these issues.)
One way of looking at is is to import some additional test of triviality. My initial reason for resisting this was Papineau's point (made on his blog, not in the TLS) that there is nothing essentially trivial about sport. (He does not consider 'sport' to be a sub-category of 'game', but let us leave that to one side.) I thought it right to separate 'games' from, say 'work' while remaining agnostic as to whether the professional sportsman or chess player is wasting his or her time. It seems to me that we need a value-free definition of the activity before deciding that issue.
I suspect that the answer lies in the word 'play', which is the correct verb to describe participation in a game. So, for example, we can imagine someone in 18th century London who sets out to become a gentleman in a true Lord Chesterfield sense. He considers this something worth doing in its own right, and not for some ulterior purpose (let us imagine that he already has wealth, titles and a position in society). He is not playing. Then let us suppose someone with a time machine who fancies visiting 18th century London and establishing himself at the pinnacle of respected society. He has no aim in mind other than to have fun (e.g. no academic anthropological or historical intentions). The two men carry out the same activities and in each case for their own sake, but the second one is merely playing. (Query: what if the time machine broke and the second one could not go back? what if he knew beforehand that he would not be able to go back?) The concept of 'play' imports the necessary distance between 'games' and the ultimately worthwhile stuff of life itself.
I do not think that 'play' necessarily imports any notion of triviality. There is clearly a high degree of overlap between play and trivial matters, but that is unsurprising as there must be a large amount of ultimately trivial playing of games (or sports). However, we are all aware that a game can be played seriously or in earnest. There are high-stakes games, and not just ones where a lot of money is at stake: consider local derbies in football or an India-Pakistan cricket match. Moreover, Papineau would add (and I am minded to agree) that there is something inherently serious and worthy of respect in the highest achievements of sportsmen, albeit they are only ever playing. I think the concept of 'play' is one which leaves open the question of whether it is ever right that a game should be treated as serious in any of these senses, whether i.e. play can or should be other than trivial.
I don't think any of this affects the point I was making in my earlier post. Indeed, it is perhaps easier to see 'brilliance' as a quality of 'play' than of anything else. For example, there is a faint suggestion that there are 'points for style' available for something that might be categorised as 'brilliant', and that seems to fit naturally into playing.
Finally, I will spare you thoughts on playing the game in Vitaï Lampada and on climbing Mt Everest 'because it is there' (not playing at all, and yet ...) and leave you just this: although these seem far from our starting point (academic philosophy departments), we still seem to be stuck with the crazy things that men get up to.