The judicial power extends to cases affecting ambassadors, other public ministers, and consuls. I would consider the President or President elect to be “other public ministers”. Cases affecting those people fall under the original jurisdiction of the Supreme Court.
In addition, there are “controversies to which the United States shall be a party”. Who exactly is “The United States”?
Read the Federalist papers. "Public ministers and consuls" was 18th Century-speak for foreign diplomats.