The only difference between the alpha and gamma male is that the former is successful and the latter is not; their attitudes are fairly similar.
Likewise, beta males have more in common with women than with alpha or gamma men.
For women, it is the contest within the harem to achieve “favorite wife” status.
Modern humans are generally impossible to classify as “alpha” or “beta”– society strongly encourages us to be beta, but both strategies live within our genetic lineage and tendencies.
Our term for a person with overbearing alpha-male traits is — a person with narcissistic and promiscuous tendencies, lacking empathy and conscience.