I think the word “qualified” is key. It means that a candidate for Senate must be 30 before he takes office, President must be born in the U.S. and be 35, etc. Some might maintain that the 14th Amendment “disqualifies” Trump, but that is sheer fantasy, on its best day.
“Someone please make sense of this:
In New Hampshire, a person whose name was not printed on the official state primary election ballot of a political party shall not be entitled to the nomination of that party for any office unless the person received at least 35 write-in votes or write-in votes equaling 10 percent or more of the total votes cast for that party on the state primary election ballot, whichever is smaller. If a person is disqualified from a nomination in accordance with the provisions of paragraph I, then the nomination shall be awarded to the qualified person who received the highest number of votes, provided that person received at least 35 votes or votes equaling 10 percent or more of the total votes cast for that party on the state primary election ballot, whichever is smaller1.”
Well in my opinion, this would apply only to state offices, since a presidential primary is not for a state office but for choosing delegates to a party convention.