It's not a new candidate. The elections are held, and if the elected is deceased at the time of the inauguration, then the established process to replace a deceased candidate kicks in.

That's the law as it currently stands, but it has never gone to court in the case of a Presidential election, so there's wiggle room for new interpretation, but no reason to believe the courts would go against current case law for lower level elections.

Not that it matters because President Trump won. We don't actually need the media to admit that he won for that to be a fact.