I don't think corporation implies for-profit. In my eyes, corporation refers to a large organization with some self-serving motivation which is not necessarily just money. Being a non-profit just so happens to be the best vehicle for this motivation but it doesn't mean that the motivation doesn't exist.

at least in america, in common discussion outside of legal/highly wonky circles, referring to an organization as a corporation almost always implies a for-profit corporation, with (literally) vanishingly few examples of the contrary in popular knowledge (RIP CPB, may you return someday).