Whether that makes it a "right" depends on your stance on things like positive versus negative rights. I'm arguing that a system that doesn't provide that to regular people is broken regardless of whether it is a right or not.
[1] By goals in life I do not mean things like "I want to own my own island" or "I want a penthouse in Manhattan". Rather I mean something along the lines of "I want to live somewhere that I can go hiking everyday" or "I want to live in a cosmopolitan city".
I don't know where the line is, but if you say the basic right is just "house", and that gets enforced, someone's going to try to draw that line as low as they can. Probably a few developers try to argue that if everyone gets a house then zoning laws need to be relaxed so they can afford it, and (hyperbole) we're back to windowless apartments with one room per family and one bathroom per floor.
For example, if a group of billionaires bought up all of the property in New York City that would then mean that there wouldn't be any left for anyone else.