We should use chimpanzees. The popular definition evolved pretty much indepdenently of the science, unfortunately [1].
Management texts have tried toning this down, particularly in the gender-equality years. At its nonsensical limit one wound up with alpha = leader, which is tautologically useless as a tool for explaining leadership.
The term probably belongs in a bin. There are deep social lessons we can learn from observing chimpanzees. (Or even wolves.) But they're not going to condense into a single term, certainly not one that's been through the 4chan and partisan ringers. Even among chimpanzees, we see a variety of tactics used to achieve dominance, including groups of chimps banding together to topple a leader.