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There is nothing fair about a state vote corrupted by voices outside of the state, let alone outside of the country.
A free and fair election is about ensuring that eligible voters are informed, that they have access to the ballot box, and that those ballots are accurately counted.
You may or may not like what's going on in New Hampshire, but if you aren't a New Hampshire resident with voting rights you don't get to have any say in their affairs.
But under no circumstances should you try to unilaterally influence or coerce him in some way. That's overstepping the line.
But, since things are interconnected, and a state isn't just some lonely abstract entity, isn't in your interest to try push for things that are good overall?
Why shouldn't I try to convince people that a certain change is a good thing, even if that change doesn't influence me directly?
States are separate for a reason, the people of each state want to do things their own way. For the things we can all agree nationally there is the federal government, but for everything else it's separated at the state level so we step on as few toes as possible.
Spamming a New Hampshire state representative when you aren't in New Hampshire, let alone not in the US, subverts democracy by violating state and possibly country lines.
What line?
It's a dangerous territory you're trying to propose.
What OP and the article are asking is for someone in, say, Belgium or Canada or Texas to go and contact a New Hampshire state representative about a strictly New Hampshire state affair. Talk about making unnecessary and inappropriate noise for New Hampshire's democracy.
