A market in this case isn't a literal street market with vendors hawking their goods. The word "market" describes the relationship between people who have more than they need selling to people who need and would prefer to exchange their money (or vouchers etc.) to acquire it.

Housing can't not be a market anymore than food or labor could not be a market. It's like saying it's warped that water evaporates and becomes clouds and turns into precipitation. It's a word that describes one of the natural systems of how the world works.

Even in communist societies where the State owns all the land and all the housing and decides how to distribute it, you still have a State-owned-and-directed market between citizens who need housing and a State that has excess housing and provides it to citizens.