Since apparently I need to clarify that I'm not into all those games and manipulation, here is my definition:
An alpha male is the one who has taken responsibility for the leadership, protection and provision for his family(group, tribe, etc), thereby taking that burden off of his mate, children, elders, etc. His is focused on the welfare of those he loves, more so than his own. While others contribute, often significantly, the ultimate responsibility is his. He must make the decisions for the good of everyone, though often with much input from others. Those who handle this responsibility well are respected.
In the modern world, with all it's silliness, sometimes this translates to the early stage of relationships as ignoring silly drama and being very direct, and not allowing yourself to be manipulated in any way, intentional or unintentional.