I heard the term used by Noam Chomsky to describe himself. Is this his own term or a mash up. Came very late to philosophy, and I see possible links to the under pinnings of Anarchism and Socialism.
I am not so familiar with Chomsky, but I think I could be a bit familiar with the anarchism itself.
Directly answering first to your question,
Is an Anarchosocialist a philosophical term or a political term?
Neither, but since the anarchism itself as I describe later involves the total abolish of the any existing entities, that hinders men's "freedom" from outside, including the country, so it might be safer for me to say it is rather more philosophical.
His note on Anarchism, quoting mostly Daniel Guerin.
Daniel Guerin : http://en.wikipedia.org/wiki/Daniel_Gu%C3%A9rin
In the middle, he is putting Engels to Bakunin ( probably the most famous anarchist in the centuries )
Engels, in a letter of 1883, expressed his disagreement with this conception as follows:
The anarchists put the thing upside down. They declare that the proletarian revolution must begin by doing away with the political organization of the state....But to destroy it at such a moment would be to destroy the only organism by means of which the victorious proletariat can assert its newly-conquered power, hold down its capitalist adversaries, and carry out that economic revolution of society without which the whole victory must end in a new defeat and a mass slaughter of the workers similar to those after the Paris commune.5
In contrast, the anarchists -- most eloquently Bakunin -- warned of the dangers of the "red bureaucracy," which would prove to be "the most vile and terrible lie that our century has created."6
Even though K.Marx though "at the final stage" the abolish of the country is mandatory to construct his "communism", Bakunin on the other hand said nothing about "what kind of "environment" would we live if we take the anarchism". Bakunin only criticized Marx. His "goal" seems to me, literally a "complete anarchy", no establishment existing, whatsoever that hinders human's act.
Sooooooo, I said a bit long, I think it is more philosophical rather than political, since when we talk about the anarchism, since there is no authority or entities whatsoever, only what I can imagine in the anarchism is just a bunch of groups ( even the "group" may not be appropriate to them ) of primitive human kind, such as picking nuts from trees for food, there may be not "hut" to live, but rather live under somewhere beneath the trees, urinating when they like, almost to way back to homo-sapience like, to me.
I hope to any extent I could answer in some way.
There is no "or". Can it be studied by philosophy? There it is a philosophical term. Can it be studied by political sciences? There it is a political term. Looks like it is both.