Employee-owned companies and co-ops are still highly capitalist though.
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.
Even from a Marxian perspective, there's a sense in which worker co-ops embedded in capitalist markets are still ‘capitalist’— they're still subject to the same kinds of competitive pressures as capitalist firms. Even for socialists and people interested in worker co-ops as a basis for moving beyond capitalism, something like ‘do non-capitalist firms even exist today?’ is a legitimate question.
Marxist economics is not against competitive markets. It’s about who owns the enterprise, the means of production, as the person you’re replying to was stating.