That would be a form of government, crude and rudimentary as it is.
alpha male status can only be achieved if a group exist.
and that's really absurd, I was joking that a chief and medicine man was government
How is that absurd? The chief would provide the laws concerning conduct of eveyday life and the medicine man would provide laws concerning religion.
It all comes down to how you define "government" and "civilization". The definitions of those terms are not all that clear.
Certainly when any group of people agree to abide by the decisions of a subset of the population that can be called "government".
"Civilization" is a more difficult concept to define. To me, civilization implies that a group of people have formed a stable community that has persisted through multiple generations and has maintained a common set of guidelines that is used to govern the community that those people have formed. It also implies that this group of people have created a persistent culture represented by the creation of persistent artifacts. Both of these types of persistence require a reliable source of food so it seems to me that farming is a prerequisite to any civilization.