The guy would have standing to sue as a member of the Democrat Party and as a Voting Citizen of the United States. As a Democrat he would be compromised by his party nominating an ineligible nominee. As a US Citizen his rights would be compromised by an ineligible nomination by disenfranchising his vote.
There is certainly standing. If there was no standing the TRO would have been dismissed on that basis. The Judge makes a determination of standing before issuing any ruling. He denied the TRO but held open the Motion for Injunction until the other Parties have been served.
I wouldn’t dismiss this suit so fast. My guess is that the Republicans have been waiting to hit him with this after the nomination anyway.
Sorry, I don't think that this gives you standing. Standing requires individual, particularized harm. What you described is not; rather, you've essentially described Flast standing, in which everyone has the same basic injury. That doesn't fly outside of establishment clause cases.
To clarify my point, take a look at the Court's decision last year in Lance v. Coffman, which denied standing to Colorado citizens to challenge Congressional districting. It is precisely on point. Here's a quote:
"[A] plaintiff raising only a generally available grievance about government - claiming only harm to his and every other citizen's interest in proper application of the Constitution and laws, and seeking relief that no more directly and tangibly benefits him than it does the public at large - does not state an Article III case or controversy."