The math on this is easy. Take some reasonable values for what an average person can lift, let’s say 10kg lifted 2 meters high. In that case your maximum potential energy (mass * gravity * height) would be 196 joules (you can’t convert it all to useful work, so in practice it will be less). Joules = Watts * seconds. The first low power LED I googled uses about .15 watts, so you’d get a maximum of 22 minutes of light. That’s close enough to what they are claiming. It would be a pretty simple circuit, I don’t see any reason they couldn’t make it in volume for $10.