The OP is probably understanding "capitalist" in the sense of Marxist economics, wherein surplus value generated by laborers is extracted by investors. In that sense, co-ops, where the workers themselves maintain complete democratic control of what happens to the entirety of the fruits of their labor, are very much in contrast to a capitalist business. Whether you think that is a meaningful/useful distinction probably depends on how seriously you take the tradition of Marxist economics in the first place, but given the context of the conversation, those seem like pretty reasonable examples.