The alpha male is by definition the HNIC, the leader, the head of the pack in the animal kingdom.
From what I can see, humans on the internet talking about how alpha they are, tend to be emotionally and often physically frail high school kids who pride their self esteem on material things and having sex with easy, mediocre bitches, who also have low self esteem. Humans in real life talking about how alpha male they are, tend to be meat heads, those who go to the gym not because its a good thing to do for your body, but for self esteem issues, in other words the sake of creating a tough exterior to hide mental and emotional frailness.
Looking at who is an alpha male realistically, I agree with whoever said different people are alpha in different situations, I think any of us who are successfully social and/or intellectual have been in the position of alpha male at various times.
I think there are things that come above being alpha in the human realm though, I believe enlightenment > alpha lifestyle. But you'll never hear kids on the internet talk about how cool prospering in positive energy is, when you are 15 it is just not as cool as fucking bitches having expensive things.