How does a moving magnetic field cause motion in the Al strip rotor?
Moving magnets create eddy currents in the aluminum by electromagnetic induction as explained by Faraday's law of induction. Lenz's law essentially states an effect of Faraday's law.

The demonstration essentially shows an eddy-current clutch or coupling that is similar to an eddy-current brake. The same principle is used in a mechanical speedometer. Variable-speed drives based on this principle have been manufactured for about 80 years. Here is an explanation by a successor to the company that was the original manufacturer of eddy-current drives.

Although there are similarities between this and a rotating disc watt-hour meter, the meter is more like an induction motor. Here, a magnetic field is rotated by a motor. In an induction motor or a watt-hour meter, AC currents create a rotating magnetic field.