A lack of belief among some individuals matters, but not enough to stop a god from being a god. Because, as you say, gods are social constructs. If we consult Merriam Webster and skip the silly monotheist definition, a god is “a being or object that is worshipped as having more than natural attributes and powers”. Note that this definition doesn’t say the being must actually have these powers. They must only be worshipped as such. The belief is the important thing to the definition, not the truth. This is because divinity is socially constructed. You can’t deny a god’s divinity except by denying the faith of their followers. If you accept that the worshippers really do believe their god is a god, you must accept that the god is a god. They may well be an undeserving god, or a lying god, or a false god, but a god they still are. Divinity is like a job. If everyone agrees that Mr Smith is a plumber, and his boss pays him to fix toilets, then Mr Smith is certainly a plumber. It doesn’t matter if Mr Smith has never fixed a toilet in his life, society has decided he’s a plumber. He could be an incredibly shitty plumber who doesn’t know anything about pipes, but he’s a plumber.