i completely agree with LoveJunkie.
you lowered both your value, and the other guy's.
you both came off as extremely immature and battling for her attention. lame. like 2 guys in spandex having a flexing showdown at the gym.
the difference between you and the other guy is that you kept on being a dick after he pretty much stopped and then apologized to "Kate", in which he admitted fault and made himself seem more mature by acknowledging it.

so yeah, you lost the "battle", mate.

best way to deal with amogs isnt to flex your muscle or to try make them look bad, you either try to befriend them (shows social intelligence, i suppose) or just leave them to dig their own holes.

the "cool, man" response.

amog: you look gay
afc: blah blah blah, you look gay, blah blah blah, flex muscles, blah blah blah
pua: cool man *return to conversation*

the afc is wasting energy and just making himself look bad - which is what chaz did.
the amog will most definitely respond with a counter attack, making himself look bad.
the pua shows that his frame isnt shaken, he's above name calling and bickering and effectively shows that he IS, in fact, the alpha male without having to waste any time and energy and without having to attack the amog.

something to keep in mind:
"Hence to fight and conquer in all your battles is not supreme excellence;
Supreme excellence consists of breaking the enemy's resistance without fighting." - Sun Tzu (The Art Of War)