Augustine here uses one of the founding stories of Rome (whether myth or historical account hardly matters) to further expose the fundamental nature of the city of man. Where the Romans would look at their own past and their city through the filter of ideas like "'glory' and 'victory'," what we really see is that the city of man is driven by power and the lust for domination. When we strip away the glitzy surface rhetoric with which we adorn ourselves, when we "tear off the disguise of wild delusion, and look at the naked deeds: weigh them naked, judge them naked," we find that the true motivation of mankind is for self-glorification. Hobbes had it right when he said "I put for a general inclination of all mankind a perpetual and restless desire of power after power that ceaseth only in death." We all want to make ourselves look amazing, to be as gods, and just as the Romans sought out a war with Alba Longa (which as Augustine points out was Rome's parent-city, and so adds parricide to the mix) so we will go out of our way to promote our own ego under any and all circumstances.
Again, we're reminded that if there is to be any hope for mankind it can never come from the city of man. Even when it appears to be at its best, this world slays the innocent (as with the widow of the Curiatii) and never stops longing to unseat God from His throne.