has you put a club over your shoulders and grip it like a military press. This induces anterior pelvic tilt. Your exercise then has one move the trail elbow toward the navel with fixed arms. I would call this a side or lateral bend. I fail to see the difference between your exercise and this short description of what is referred to as the spine engine theory.
That doesn't mean that I agree with all of the points of the spine engine theory. I agree that the movement of the spine doesn't cause the legs to move, but rather they are forced to move to compensate for the side bend. Otherwise you would topple over. I also think that pro golfers actively use their legs They are not passive as the spine engine theory seems to dictate. The fact that this movement induces body rotation is my real point, and I think that it supports your earlier statement: "While there is some rotation it is not primarily a rotational movement that requires either hips or shoulders to be open to the target at impact."