Yeah, I agree actually. The article seems to conflate socialism with "when the government does stuff". Socialism is, instead, just the democratic organization of an economy. Thus it's incompatible with liberalism.

Take the Zapatistas in Mexico. They control an anarchist autonomous zone, and their economic system is socialist in structure. Socialism and anarchism are perfectly compatible, though socialism is not necessary. One could have a communist economy that functions as a sharing or gifting economy instead, for instance.

Or, look at the autonomous zone in Syria, Rojava. It is also founded on anarchist principles, and once again, its economic structure is socialist.

Basically, if you're going to take an anarchist stance, it's also going to be anti-capitalist. That's why anarchists universally don't consider anarcho-capitalism to be a form of anarchism, because that ideology (which is mostly a byproduct of online tests like the political compass which nobody should take seriously) doesn't actually apply the anarchist critique to capitalism (which is often its primary target).