The motion of objects occurs because all objects emit and absorb gravitational wave energy all the time, and so any point in space will have a unique wave energy density profile surrounding it. Since any object in question both emits and absorbs wave energy, and moves in the direction of the highest source of inflowing gravitational wave energy, space can be referred to as a medium that is filled with gravitational wave energy, not a fluid medium it the strictest sense.
But for space to be the medium , means that space has physical properties .