How does cid make power?

This is why dyno runs are now done at a rate of acceleration. This is programed into the dyno controls. The engine is loaded to the start RPM and then the dyno controls the RPM increase per second as programmed. This is more like how an engine under acceleration runs, and the dyno software records the torque every say 100 RPM and calculates the HP from that. It is not possible to measure HP directly, only torque.
HP has been used as a value people could wrap their heads around due to indoctrination. An old steam Rumley tractor with 15HP will pull a 400HP modern 4WD tractor backwards due to torque and weight. If it was HP doing the job, the modern tractor should get it done.
Mazda is starting to push advertizing to promote torque for street. Torque gets you off a red light quickly and easily and provides the nice push in the seat of your pants coming out of a corner. Big HP lets you drive 200MPH at Daytona or Bonneville, but not really useable in street driving. It is the torque that gives the calculated HP numbers.

Torque is not accurately measure unless one stops the engines acceleration. The rate is used to simulate a car accelerating, and the torque is backed out of the force required to hold that rate. But the actual torque spit out and graphed is not what is measured.. It can't be, otherwise the engine wouldn't gain revs. Instead one can use the rate and some constants to figure out what the stopping torque would theoretically be and good software can be close, but I'm sure not all softwares are equal..