It still leaves a few political perspectives out. It isn't much of a reach to call Marxists "statists" but you'd have to lump then together with fascists and that's a bit of an oversimplification. And if you are an anarchist and answered the questions based on that perspective it would probably list you as a liberal. Maybe the graph should include one or two more axes...
A commie would be a left leaning statist and a fascist would be a right leaning statist. Those are covered.
Until you consider non-statist commies, like anarcho-communists.
I find this a contradiction in terms. The survival of any group would require protection from other groups. Let's say that you existed outside of a government and formed a commune with 2000 of your closest friends. What is to stop a nation near by from coming in, killing all of you, and then taking all of the goods you had produced? A disorganized band of communists with no formal training would not fare well against a well trained, well armed, formal military. Also, how would an anarcho-communist society ever keep religion from becoming government? In the anarchy following the fall of the Roman empire, the Roman catholic church took power before the feudal system took hold. Would this also be prevented by a disorganized militant mob? The second you bring order to a military you've created government. This cannot be avoided.