Answered already, but clarifying.
Correct that a law in NH can't prevent Indiana from doing something.
It compels the Office of the Secretary of State (or whoever governs elections in NH) to be first.
Well yeah but you don't have to follow that too far to see the inherent absurdity.
If three men who work at an office all declare rules for themselves that they have to be the first person to walk through the front door in the morning... it doesn't take a genius to see how that isn't going to work even if none of the 3 try to tell the other 2 what they have to do.