Well yes and no.

State funded (public) universities are officially not-for-profit. However they are no charity and behave themselves as a for profit organization. They maximise their amount of students, maximise their quality and minimise costs, they are at risk of going bancrupt and have many deals and ties with businesess. Their quality of research indirectly attracts students and with that money.

Besides the world surrounding research is definitly for-profit mostly, journals and publishers play the key role and are generally for-profit. The only people not really earning well on their efforts are the researchers themselves.