Nothing in either of my previous posts referred to compression checks.
You are of course correct in saying that a simple compression check does not provide an accurate indication of power output.
If compression checks are carried out using the starter motor to turn the engine, then clearly the rpm will be very low. Under these circumstances the compensating effects of the pressurised crank case will be minimal, so leakage past the rings will probably be much greater than when the engine is actually running.
But if the leakage past the valves or the piston rings is sufficient to reduce the compression when the engine is running, then the IHP that is being generated at the faces of the pistons will be reduced. And unless the wearing out of the sliding surfaces has reduced internal friction sufficiently to fully compensate for this loss of IHP, then the power output will be reduced.