It seems pretty clear to me that the author means "has meaning" means "is important".
So two things can have meaning and mean two different things.
thus "if everything means something, nothing means anything." is wrong because 'meaning' as a property is not enough to establish that all items have the same quality and thus the quality does not serve to distinguish and becomes, excuse the phrasing, meaningless.
Our quest for “meaning” is a quest for what is important to us that we also have some agency in.