The relativistic principle is part of Newton's mechanics. This principle states that it doesn't matter what reference frame you use to measure and interaction. The outcome of the interaction is depends only on the two bodies themselves. Maxwell's equations retain the relativistic principle from Newton. They were not dependent on the motion of anything in between.
Special relativity is also limited to non-accelerating reference frames.
Now in order to describe the actions of the bodies, we also have to take into account the accelerations of our reference frame. These two forces do not exist in nature. They have nothing to do with matter or energy. Moving objects will appear to accelerate along this curvature without experiencing a true force. Newton's gravitational force equation is an empirical relation as to what the force must be if the planets are to orbit in their observed fashion.