that's a definition that is lacking, though. it's less that it's wrong and more that it's kind of over-specific. and, in the end we're talking about splitting hairs. when you talk about "using government to ameliorate social inequalities", it's not clear what that refers to: parliamentary democracy, workers co-operatives, council democracy. if you restrict it specifically to parliamentary democracy, you get the kind of liberalism that exists in canada. if you're a bit more broad about it, you're constructing anarchism.
i consider the opposition to rights, as articulated, to be marxist, not anarchist. i'd actually point to this as one of the differences between anarchism and marxism, and why anarchism is superior.
nor do i think it's off-base to suggest that anarchists are hegelians or that they believe in the inherent goodness of people.
to me, the only serious defining difference has to do with private property. liberals are, of course, advocates of private property; anarchists are generally not. but, there's a spectrum, there, and degrees of support - enough that if you want to be as general as possible, it sort of fades away.