How does cid make power?

100%

when people say torque engines they actually talking about low rpm hp.

I'll also say that it still 'depends'. I agree that 'low rpm hp' engine is exactly what you get with a 'torque' motor. The reason 'it depends' is because dynos can run at various rpm rates, and that rate can have a significant effect on the outcome. A slow ramp rate will let a lazy build look good on paper (bigger numbers), but will tend not to perform well in a light (fast accelerating) car.
A quick ramp rate can make a decent build look lazy by 'outrunning' the engine's ability to accelerate. A quick ramp rate could also hide harmonics in the valvetrain though by quickly accelerating past trouble spots in the rev range.

What makes sciencing it difficult is that the way 'torque' is captured is back-computed from the dyno resistence necessary to hold that ramp rate. How the dyno back-computes could be done in a few different ways, which is probably just one of the variables behind dyno differences.