The formulators of the trinitarian doctrine didn't conceive of Theos as a title, but as a being (essence, substance, οὐσία). They also described the existence of persons of that being as all dwelling fully within each other: perichoresis, following mostly John's gospel: "Do you not believe that I am in the Father and the Father is in me?" Rendering the word God as a title ignores all the richness of the actual trinitarian theology. It resolves an apparent paradox, but at the expense of the actual trinitarian view.
From that perspective, it made sense to them to say that Mary is the mother of God, because in Christ "all the fullness of the Deity dwelt bodily". They still are only referring to Mary as the mother of the incarnated God, but that incarnation is fully God. "If you have seen me you have seen the Father", as Jesus said.