It's gearing that amplifies torque. Power is just a measurement of how quickly you are generating that torque. Imagine torque as single punches in a bar fight, each one has a certain "hit". The brawler who generates more power is the one that can land 5-blows/sec vs. 3-blows/sec for the other guy. So even though each punch is exactly the same force, the one landing more blows per second generates more power.

So it's actually the torque that is measured. If you were to measure anything on the bike, you'd measure torque at the crank or at teh rear wheel. Then combine that with a timer to measure RPMs and power is then calculated. Power is basically torque per unit time.