The Buddha was male, so was he an "alpha male"?

Not all Buddhist agree on many, many things

There are martial descriptions of Buddha — he is the Jina, the conqueror. See John Powers’ A Bull of a Man that discusses the imagery of Buddha’s masculinity. Julius Evola, the Italian fascist, wrote a book, The Doctrine of Awakening: The Attainment of Self-Mastery According to the Earliest Buddhist Texts, which highlights passages that make Buddha sound macho, comparable to Nietzsche’s Ubermensch as it was understood at that time.

As is well known, the Bodhisattva Avalokitesvara = Guanyin morphs into a female in E Asia. There are passages in some Buddhist texts that dismiss difference between male and female, and others that emphasize that only a male can become a Buddha, regardless of how many female lives he may have had in the past.

For what it's worth, I think the bodhisattva vows are counter to the macho need to play to win, to lead others rather than assist their self power, etc.. ymmv, maybe dependent on whether you see the Buddha responding to others according to need, as I do, or capacity

the lion's roar will appear. He will use the power he achieved in deep meditation to benefit countless beings

but this doesn't preclude courage, or skill.

No self may imply submissiveness, in some ways: not putting your own "me" and "mine" first.

'Alpha male' is strongly tied to the senses and wealth, status etc.. Which clearly Buddhas reject as mundane.

I think you got the definition of "Alpha male" wrong by associating it with putting "me" and "mine" first. In dire situations like that scene in the Titanic when it starts sinking, a coward is always the guy who puts himself first, and he'd have no problem with kicking and pushing women and young children aside to secure a spot on a life boat, Or when a defensive position under heavy attack from the enemy, the coward always runs first while the alpha male stays and fight. It'd take the tremendous courage of an alpha male to be the first guy to enter and the last guy to leave in dire situations. Similarly, real Buddhist asceticism is certainly not for the faint of heart, and so in that regard, we can say the Buddha was THE alpha male among all alpha males, for He was the one who defeated Mara and his armies of lust, hatred, and ignorance; while we all more or less are still slaves bowing down to his power!

The traditional description of the Buddha's physical characteristics include "well retracted male organ" -- so perhaps "androgynous" in that sense.

I understand "alpha" as being a social adjective -- there are alpha males and alpha females -- and the Buddha was "alpha" in that sense i.e. socially: a leader, able to dominate (confidently and indisputably lead or teach) any assembly (of people) and any individual, with kings too (and gods) being respectful.

I think it's rude and missing the point to be asking about people's genitals, but since you ask.

You mentioned in a comment,

please be aware that 'alpha male' derives from animal behaviour, and the need for access to women's bodies / physical intimidation over other males. so you side with the 'macho' buddha

I don't think that's how the term "alpha" is applied to human beings -- some alpha humans might be faithfully married or celibate -- IMO it's just a matter of being recognised as socially superior or second to none.

For example here's a quote from a sutta, MN 12:

Sariputta, the Tathagata has these ten Tathagata's powers, possessing which he claims the herd-leader's place, roars his lion's roar in the assemblies, and sets rolling the Wheel of Brahma. What are the ten?

To answer some of the details in your question, I think it's that the Dhamma (the Buddha's doctrine) is seen as being "best" -- that's why and on the subject of which the Buddha dominates an assembly -- the Buddha is described as "an unsurpassed teacher of Gods and men" but the Buddha himself reveres the Dhamma, see Reference request for "the Buddha takes the Dhamma as his superior"

You might see the Buddha as "submissive", e.g. not flaring up when insulted -- see SN 7.2 -- I wouldn't call that submissive though, I see it as self-controlled, heedful (keeping your eye on the prize), and skilfully cooperative:

You live for the good of both
— your own, the other's —
when, knowing the other's provoked,
you mindfully grow calm.

There's a fair bit of doctrine about not arguing with each other, and about how arguments (including arguments about the Dhamma) might be associated with conceit.