"I don't have a problem with the part about generating electricity - just the propulsion side of the story. So this wire repels the earth's magnetosphere with sufficient force to raise the spacecraft to a higher orbit? Is that correct? Or is it something different?"

Well, there are two parts of the propulsion part of it- lowering and raising the orbit. If you are generating electrical power and using it (or just getting rid of it) then you will lose orbiting speed (you simply can't get energy for "free"). So if you understand how it can get electrical energy from a wire in orbit, then you do understand the propulsion side of the story- at least one 1/2 of it. And if you can get electricity from a wire, you should be able to give electricity to the wire.