Hm. Every example of a "game" I can seem to think of involves some sort of arbitrary, to use another hard-to-pin-down word, rules (exempt for game=prey, but that, I believe, is a homophone).
David Webster, in his The Fall of the Ancient Maya, defines a 'civilization' as a society that exhibits all or most of a list of features, which notably includes cities, writing, and monumental architecture. Of course, his concern was differentiating 'civilized' peoples from whatever is the currently acceptable term for barbarians, and so his definition is of little use for telling whether Canadians and USAmericans belong to the same civilization or not.
The traditional definition of a city would be the Temple, the Palace and the Granary - ie. a permanent settlement that is simultaneously a religious, political, and economical centre. Webster, incidentally, would exclude the Maya centres of the Classic (Tikal, Palenque, and the rest) from the category, essentially because he does not think they functioned as economic centres.