The definition of alpha has been skewed over the years due to the PUA community and the fact that actions, people, or emotions are one end of the "alpha-beta spectrum" or the other. Its polar, and its not necessarily correct. Now thats not to say I don't value "alphaness", or try to be a dominant and exciting man, but the fact of the matter is that nothing in life is cut and dry. Everything is a shade of grey, there is no white and black. A career dominating male may go home and be whipped by his cheating wife, a man that is proficient with women may make $9 an hour working at a fast food joint.
Read this article and decide for yourself:
http://markmanson.net/butchering-the-alpha-male
You'll notice that nobody is "alpha" or "beta" 100% of the time.
You'll also notice that extrinsically, someone may appear to be alpha, but internally, there is issues that have to be solved.
What I would personally consider alpha is a man who is well rounded, excels in certain facets of life (women, money, style, leadership, business, intellectual pursuits), is proficient in all others, and his internal voice lines up with who he is on the outside. You need to be a man; be loyal to your friends, be a man of your word, be brave, and be always improving yourself. You needn't give a fuck about what others think of you, keep your head up at all times, and understand your own value. Be a leader, be humble, find mentors who have gone down the same road as you, and have passions that you pursue, regardless of what anyone thinks. Lastly, tie this all together with an open mind, the ability to speak this mind, and standing for something that you believe in. If you match all the above criteria, then you sir, in my eyes, are an alpha male.