I think the article meant to the nomination as a whole as the "primary", or otherwise the article was edited poorly or something like that, or Biden made an oopsie.
No, they're just very picky about these things! New Hampshire loves to bill itself as the "first primary" — state law actually specifies that it must be held a week before any other primary, and only the fact that Iowa is a caucus state prevents a major fight over who gets to be first every time. It does not make much sense to me, but I haven't had my brain rotted by decades of maple/corn syrup, and those are the people in charge for the moment.
