That's not an alpha male. What you have described there is a wanker.the alpha male is that guy that;
parks sideways , taking up more than one parking spot. or in a handicap zone, but has no handicap.
takes the two car length space between you and the car infront of you, then slams on the breaks to get you to back off his ass.
goes well beyond the firm handshake, and tries to break as many bones in your hand as possible.
gets into the 10 items or less lane at the market with 20 items.
fires the dedicated lifelong employee without benefits to hire a slacker for 1/4 the price.
becomes temporarily deaf when a woman says "NO!".
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urban dictionary hits the alpha nail on the ever expanding head several times...
"A domineering and aggressive male. Instinctually forces his will upon other males and females to get his way through any means necessary, including violence. Unhibited and primitive."
"The alpha male is an act that is performed by males usually in their teens and twenties who act tough, are loud, and have to be the center of attention or they feel insecure. When a man is successful and in his thirties he no longer acts this way because he has grown up and realized that the entire alpha male act is phony. When was the last time you saw a rich, successful man try to pick a fight??? Never. The only guys that do this are the losers that go to bars to take their anger out because they are angry inside for going nowhere in life."
"Like a real dictator, some megalomaniac who thinks he has some special right to run the show. Has only as much power as people give him in their minds. You choose to obey him, he has power. You choose not to, he has nothing."
"Those who are born feeling that the world just "isn't right" and it's their job to make it right. Will do anything to gain control of people and bend them to their will. Forces ideologies on all people, friend and foe, domestic and foreign.
Has no sense of reasoning except rationalization, which may you note is coming up with reasons after-the-fact. Completely and totally reactionary.
World renowned for creating illth (in place of wealth) and convincing people there is really wealth.
Usually identifiable by their ape-like complexion and ape-like actions. (They're a regressive force in evolution - things always flow both ways)
Stereotypically, what every marine wants to be."
Here's a place where you can start getting a clue to what the phrase means:
Alpha (ethology) - Wikipedia, the free encyclopedia