The center of mass is located closer to the higher mass star.
Moreover, In a binary system, each star moves on an elliptical path. The COM sits at the focus for both ellipses. By symmetry the centripetal force on the other star will be the same. That there is no body at the center of rotation of the system doesn't matter. It's still the center of mass of the system, and the two stars are orbiting it.
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