The values and behaviours of a so-called "alpha" male according to TRP (as I understand them):

- Uses women for sex. This is contrasted with traditional masculinity since pre-Roman times, where women generally were supposed to be respected and treated with dignity (slavery existed for both genders, but chastity was always a virtue).

- Indulges himself sexually/has uncommitted sex. Traditionally the mark of a weak or dissolute man or looked down upon.

- Uninterested in relationships. This is obviously the opposite of traditional masculinity, as a relationship is necessary to have children.

- Self-interested and not selfless. Selfless service is a traditionally masculine virtue, especially in the case of war or saving others.

However

There are several aspects of this archetype that do fit with traditional aspects of masculinity. These are:

Physical prowess/dominance: Although huge aspects of this are genetic, almost anyone can train to be stronger and physically tougher than 95% of the population.

Confidence: This is hopefully self-explanatory.

Leadership: Once again, being a leader where necessary has always been an aspect of masculinity.

In conclusion, the "Alpha Male" archetype can not be considered as equivalent to a traditionally masculine male, as the archetype behaves in ways that would traditionally have been considered fundamentally unmasculine, despite possessing certain similar traits.