The link is irrelevant; the person who wrote that comment refers to himself as a Marxist-anarchist. And I would add that he's taken the most vulgar aspects of each and attempted to create an impossible hybrid.
But to get to the heart of your question: depends how you define/understand "socialism" (and "anarchism" for that matter). If socialism is characterized by a generic opposition to capitalism, then sure, anarchists are socialists. If socialism means that the state controls the production and distribution of goods and services, then no, anarchists are not socialists. If socialism means that people who have no direct access to or control of the means of survival without working or getting economic support from the state will get to have that access and control, then sure, anarchists are socialists. If socialism means that hierarchical institutions that foster a division of labor will continue under the control and direction of the best and brightest, then no, anarchists are not socialists.
As is the case with many of the questions being posed, there are at least two or three more questions that need to be asked before a proper answer is attempted, let alone agreed upon.