The Aristotelian passage is in Pol. 1253a: Aristotle compares the cityless man (απολις) to an isolated piece in a game of 'pettoi' (ατε περ αζυξ ων νσπερ εν πεττοις). The curious word αζυξ occurs at a much later period in Agathias' epigram on Zeno's game of ταβλη , where it means a 'blot' at backgammon, i.e. a single piece standing unguarded by a companion and therefore liable to capture. But the commentators are surely wrong in supposing that Aristotle had the race-game in mind; the word in the context, and the comparison introduced between the 'cityless' man and the pugnacious Homeric warrior (I agree with Jackson in assigning the comparison not to the αζυξ ; but to the απολις) both suggest that he meant the battle-game, 'poleis'.
Could fellow Agorans advise the gender of the noun? I could not find the word in any of the online Greek dictionaries.