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Seems like a professor of mine mentioned that they work on induced charge. They have an internal magnetic field and movement within the earth's magnetic field induces a current. Wonder if they'd work while the core is shifting?

Offered by Roger.

This professor is wrong. The kinetics mechanism works by putting motion into energy.

Offered by Michel.

An advertisement for the watch, explaining a little of how it works, from Seiko

Seiko has spent over two decades of research and development (along the way generating more than 50 patent applications world-wide!) to bring to the world the Seiko Kinetic watch. This is the first quartz watch that never needs a battery because it's powered by human movement! What makes this work? It can be summed up in five steps:
First, simple everyday movements of your wrist rotate an oscillating weight inside the watch.
Each movement of that oscillating weight rotates a rotor, converting the movement into a magnetic charge. Mind you, the rotor is no bigger than the head of a pin, and can spin up to 100,000 RPM!
An extremely high density coil then transforms the magnetic charge into the electricity that will power the watch.
Hang on, we're not done yet! The electrical energy is stored in a tiny capacitor, awaiting instructions from the brain of the watch.
The integrated circuit determines how much energy to store and release, ensuring precise quartz timekeeping. Precise, as in nearly 100 times more accurate than a mechanical watch.

Offered by George.