Is using a DERATE for Takeoff actually reducing the power of the engine?
I cant' give you a 737 specific answer, but how DERATE or Flex Thrust is applied generally depends on whether the engine is FADEC or not.
If a non-FADEC, it's just an FMS computed bug target setting on the N1 indicators and you move the thrust levers as required to match N1 to the bug. So it's still the pilot actually setting thrust to a lower computer-provided target than normal (if the airplane has an autothrottle system, it's the autopilot doing that job on behalf of the pilot through thrust lever servos).
If FADEC, where you (or an autothrottle system) just move the thrust levers until they click into a detent of some sort for takeoff and let the FADEC computers directly control the engines to achieve a computed N1 setting, it's the computers controlling the engines in accordance with your thrust rating selection when you ask for TO thrust.  So in that case it's the pilot telling the computers what he/she wants, and the computers do the actual work.