Taken back to its ethological roots, 'alpha male' simply means the highest ranking male within a group who has top priority for food and mating with females, usually achieved through physical dominance, sometimes bolstered with social alliances.
Human groups don't live in discrete packs or tribes anymore. There is too much globalisation that has led to overlap between groups, on a regular, habitual level, not just occasional. We all have our family groups, friendship groups and work groups and hobbies, etc. Different people can be in each group. It's no longer a given that we all live in small villages where we socialise and have children with the same people we work alongside with.
In the case of humans the alpha male of one group would naturally conflict with the alpha male of another group when the two alpha males have to meet in another setting. Nothing would get done if all these alpha males kept trying to establish dominance over each other (actually that could be true come to think of it, given the macho posturing that goes on in some gatherings... 
).
Also, human culture has other powerful social tools and behaviours unparalleled by other animal groups (not saying they're better BTW, just different) which means that we cannot really have an 'alpha male' anymore. We tend to elect leaders rather than ask them to fight it out. We don't let survival of the fittest take care of our orphaned/sick/old/vulnerable. People are appointed on the basis of their skills/who they know rather than being asked to cage-fight for that coveted CEO role, etc.
So yes, humans can have alpha males if we accept that human culture is no different from the social behaviour of any other group. Power is coveted by nearly every human being alive, even if to them that merely means having the power to control their own lives rather than being subjected to the whims of another.
If, OTOH, we'd like to think that our highly developed culture sets us apart from the behavioural patterns of other animal species (which I do) then we have to accept that 'alpha male' is simply a euphemism for a bloke who throws his weight about, aka a bully or a charismatic manipulator/leader, who could admittedly be benign rather than sociopathic but it's a very fine line and it all comes back to desire for power and control.
Suppose 'power hungry egomaniac' doesn't trip off the tongue as easily as 'alpha male' though...