There isn't a fixed definition [1]. Most definitions reference dominance, e.g. Merriam-Webster [2]. (Annoyingly, dominance also has different meanings in anthropology, animal ethology, sociology and common use.)

But due to the term being relatively new, adopted from animal ethology, co-tiopted by the memeverse and now being politically charged, you're basically walking into semantic ground zero by using the term.

[1] https://en.wikipedia.org/wiki/Alpha_and_beta_male

[2] https://www.merriam-webster.com/dictionary/alpha#word-histor...