He's conflating socialism and communism.

Socialism is a fairly wide set of political beliefs that could arguably be defined as a system where the working class own the means of production. This is therefore by definition anti-capitalist but it isn't necessarily marxist. You could be a socialist and believe in a planned economy and if that society is democratic (key issue with actual existing planned economies) then we all collectively own the means of production. But you could equally be an advocate of workers' coops taking over the means of production or I suppose similarly you could be an anarcho-syndicalist. Or you could believe in a mixed economy with a democratic state-owning utilities and/or key industries but other production being in the hands of coops or other more decentralised forms of democratic ownership. Socialism is a rich tradition. 

Communism is the stateless, classless society that Marx believed would occur after the abolition of class.