"1.4 informal as modifier Denoting a person who has a dominant role or position within a particular sphere. "
Alpha is simply dominance. If you're a top tier lawyer, you are an alpha lawyer. You get the most resources, you are looked to as a leader, people turn to you to get things done. If you're in a relationship with a woman, you're the leader. You handle the relationship, you lead it, you're competent and she looks to you to get things done. It also means you compete with other men in those spheres. Can this other guy provide more protection, more money? Does he have his life more sorted out? Is he better in bed?
Think about a friend you have who is doing really well in their career. You admire that person because they are succeeding. They are dominating within their sphere of influence. That admiration is what women are attracted to, in part. Women cross culturally and universally do not date down in social status.
Where people get confused about alpha, is associating it purely with physical dominance, tyrannical dominance only, or creating a binary in which you can only have alpha traits. That sort of caricature of alpha might be attractive to some women, but it's not necessary for success with women in general. It's likely it is harming your success with other demographics of women, potentially women you might want to date.
Not many men make it to the absolute top of physical fitness, career success, etc. And there are 3 billion women. Thinking you need to be the epitome of "alpha" to get women is insanity. You just need to be competent and aim at women within your social sphere. There are good attractive women within all spheres of society. Just because you don't have a shot with Angelina Jolie because you're not Brad Pitt, doesn't mean you're not alpha enough for women in general. Don't fall into the trap of creating all or nothing scenarios that trap you in your state in life.