Let's start with the fact that being an alpha is a whole lot more than just ordering people around or intimidating people with the threat of violence (that's called being a bully). And it's definitely more than just being able to beat people up.

Being an alpha has to do with one's involvement in a group. More specifically, it's about the helping develop and maintaining a group dynamic, hierarchy and the functionality of the group. And this not just for your own benefit.