Dear Jim,

There is a key idea, derived from ‘family resemblance’, which perhaps games do not exemplify (if you are right), but which many other groups do.   This is that what the ‘family’ F have in common is that every member of F is more like some other member of F than any member of F is like non-members of F.  Members of F naturally form a similarity cluster.   F could be a syndrome, for example, whose totality of instances have this overall character, even though there are no non-disjunctive necessary and sufficient conditions for F-membership which can be generalised to cover all and only members of F.   This notion of clustering has been developed to a high degree of sophistication from the original publication in 1963 by Sneath and Sokal of Principles of Numerical Taxonomy.  Wittgenstein was given an honorific mention on page 14.   

It could be, of course, when similarities between objects are fully mapped, that nature doesn’t have any ‘joints’ by which any taxonomy could reasonably carve it up.   Equally it could be that everything is of some kind, and every kind has an essence imbued in it by the logos.   The jury is out on that, I think.   Meanwhile, there is a massive, sophisticated discipline based on the notion you take to have no application even to its most favourable case.  I think that is because (typical) games probably do not provide its most favourable case.