Why is Tom James consider VP-elect at the end of Veep Season 4

In the last episode of Veep Season 4, they say that in the event of a tied vote it goes to the House and each state gets a vote (I guess meaning the congressmen from each state share a vote between them? Presumably they decide where that vote goes by voting?). If no one gets a majority of states, then the "vice president elect" becomes president. But given that this is meant to address a tied vote, in what sense is Tom James the VP elect as opposed to O’Brien’s running mate. And also, if there is some distinguishing factor, then why VP elect and not the president elect?

Is this a real rule or were the writers just making stuff up to fit the narrative?