I would like to make a quick distinction about alpha-ness...
IMO, a man doesn't have to actually BE an alpha male to exhibit alpha male BEHAVIOR. He doesn't have to be the biggest, or the richest, or the top of his profession, or the smartest, or the best at anything...he just has to BEHAVE as if he is the best HE can be at being HIMSELF. He needs to behave as if he knows he is deserving of a good woman, and of good sex. He should be confident. He should rely upon his own strengths, knowing he will get through any adversity. He should be able to see himself as a winner. He should know within himself that he can show a woman a good time in bed, and then be able to execute that truth.
Behavior that is not alpha-male-ness can be a huge turn off. This would include: wanting a woman to call the shots or wear the pants or tell him how to behave. Wanting a woman who is in control of the situation. Or letting a woman control the situation because he has no idea how to lead, so he feels it is easier to let her lead as she seems to be good at it. Feeling insecure about other men, in professional life or in his sex life. Feeling insecure about his prowess.
Then there is another distinction, which is that many men can learn how to behave dominantly in the bedroom only. There are many non-alpha behaving men who have learned how to be sexually dominant as part of their sex life. In my experience, men like this are rarely going to exhibit true alpha-behavior and therefore, they might be a fun time for a woman who is into being dominated in bed...but most women aren't really looking to be totally dominated. That is usually just a sexual choice of lifestyle for a woman, and not what the average woman wants. (Again, this is all coming from my own experience and opinions...not speaking for anyone else here, just talking about women I've known and my own life).
I think most women would enjoy being dominated slightly sometimes (ie: pushed up against the wall, spanked, or told "what to do" in a sexual situation, hair pulling, etc), but are not going to be into that all the time, every time. Instead, I think most women just enjoy knowing their man is capable of exhibiting this type of raw sexuality - even if he isn't into that himself all the time. Being able to exhibit it shows alpha male behavior.
Being UNABLE to exhibit a bit of rough play in the bedroom usualy tells me as a woman that a man will not be able to exhibit other alpha male behaviors....and its the overall alpha behaviors that will be (for me) the long term turn on.