For example, Joe Biden is nominated and then dies, or Donald Trump is nominated but then a court bans him from running or he chooses to withdraw.

Only counts nominees from the democrats and republicans, not third parties. Being removed in any state is sufficient to resolve YES. If the candidate is physically on the ballot but everyone knows they can't win no matter how many votes they get (e.g. they died 1 day before the election and the ballots were already printed), that's also sufficient to resolve this to YES.