What is the definition of government?
A government is a system comprised of a collection of laws outlining the hierarchy of power within a society and controlled by a person or group of people.
There are several things needed for a government to exist.
First, there must be a group of people willing to submit to the power of a controlling entity. The submission need not be voluntary. Theoretically, if even one person submits authority to another it could represent a form of government.
Second, the controlling party must have some formalized standards enacted upon the submissive group. The US has the Constitution, but an autocratic dictator might have something as simple as "do what I say when I say it".
Third, there must be a controlling party or person. This is an inverse rule of the first, but it is important. Even if a group collectively says "we want someone to tell us what to do", unless someone does tell them what to do there is no governance.
The last piece is important as well, the system must be expressed to the submissive and dominant parties. The leader must know they are in a position of power and the submissive must understand their responsibility to submit. If neither is met, then there is no government.
Those are mandatory minimums for a government to exist, but like with many things there are numerous avenues to explore to add to the list.