Re your second two points
if there are limits like disabling pvp, it is not true anarchy.
if there is a leader, there is no true anarchy.
I have neither of these, so they are not valid points
For your first two point,
Anarchy by definition is "Absence of government and absolute freedom of the individual"
You have the absolute freedom to grief and steal and kill on the server, so as such it is an anarchy server
In your first example, the play doesn't have the "Authority" to do that, authority implies the rights or rules to do such an act
If there are no rules and no governance, then there is no authority in place
