Kinetic energy is relative to some inertial reference frame. You can pick any reference frame you want and each will give you different numbers, but conservation laws should still hold in each.
Addition of kinetic energy is pretty unintuitive in this regard, e.g. when throwing a ball, the "work" done by your muscles depends on the reference frame that you pick to analyze the event.
I believe the trick here is that constant-acceleration with constant power use is due to the (puzzling) particulars that there's no ejection mass