You can call him beta all you want but you are wrong. He behaved like an alpha because he refused to be fucked by his girlfriend so he can make HIS move.
Do alphas get invited to bed by their girls? She calls you and you jump into sheets, wagging your tail like a dog? This doesn't sound to me like a alpha-thing to do. Maybe regular, casual alphas do that. But true alphas initiate sex on their own!