Obama has reached the highest position in the entire world, and twice (elected second time), so it is hard to say that he belongs to Beta group. He is very smart, intelligent, very charismatic and personal, there is simply no way to say that he is Beta...
At the same time, there are different approaches, different ideologies, believes, convictions, views...
When we take the classical "western" world so far, Obama simply don't fit the definition of classical Alpha because he has different ideology, different believes, different approaches... He is just different sort of Alpha... The classical "Alpha" in current western world is e.g. GW Bush. Or Putin. My way or highway. You are either with us or against us. You will either do as we say or we will bomb the crap out of you. This style of thinking is a style of our fathers and grandfathers. This style of thinking is what built great America.
But there has been a great shift in society, the classical western Alpha is becoming less popular. We are now more about communication, negotiation, friendlier approach, smiles and hugs... This is the future, this will be the world of our sons and grandsons...
So Obama is IMO just a preview of our future. He is much weaker, more dynamic, not so structured, doesn't have so much backbone as today's classical Alpha - yet at the same time he is much more intelligent in his approach. Think about it, the whole old establishment of current western Alphas (the whole republican congress) is unable to do anything, Obama does as he wishes and almost without any resistance... He also does "my way or highway", but on his own terms... He got all the 'old republican establishment' by their balls, they are unable to do anything because Obama simply beat them in their own game...