woah... way to complicated for me.
First Magnetic Chess Game

It looks like I mistated the rules. They should say that opposite charge attract. The diagram is correct. After 1.e4 the board is actually:

3. ... Ne7
I'm wondering about the rule "there is no check, mate, or stalemate, king capture wins." Okay, so there's no check. But I still have to stop you or you'll capture my king, right? And what if I do get stalemated? If there's no stalemate then the game isn't over. But if I have no moves what do I do?

if can't not have no moves. You can walk into check as there is no check. So if you have no moves that would be legal in normal chess, you basically lose. you have to move and then your king gets captured

I wonder if you could play this with the magnetic attraction\repulsion, down the queen lines, not just the rook.
The rules of Magnetic Chess are: