It's not really the electrons moving. It's the electromagnetic field potential that's moving. The rope is that field. And the distance it moves isn't measured in meters, but in volts. In most cases, around 240 volts (more or less...but that's a whole other discussion).
A lot of this is hard to wrap your head around because you can't physically see these forces, only measure them with instruments. We'll dive a little deeper while still trying to keep the rope metaphor going.
Imagine each electron in a wire as stationary, and all standing in a line next to each other all the way down the wire, each connected to its neighbour by a loop of rope. If you turn one of these electrons, it causes the one beside it to turn, which causes its neighbour to turn, etc all the way down. Our pulley is attached to one of these electrons. You pull the rope one way, it turns the pulley, which turns the first electron, which transfers that energy all the way down the line. How far you pull in one draw is the voltage. How hard you pull is the amperage.
This is the basis of a generator. A magnet (our pulley) is passed over a coil of wire, which induces an electromagnetic field (our rope) in the wire. It makes the electrons "turn", and sends that energy down the entire length of the wire. Nothing really moves except for the electromagnetic field.