Yes, if four people suddenly died, we would have a President who was appointed by someone elected, and then confirmed by the Senate. In theory, he would have the same views as the people we elected, and that is an awful lot of unlikely death to get there.
I am not particularly worried. There is not some huge exception that allows us to be a dictatorship.
Even the original version from the video would not result in a dictatorship because whoever was appointed president would still be bound by the Constitution and Congress. We have too many safeguards to prevent abuses.
It is more complex than that. The Constitution does say, "Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors", but also says, "The United States shall guarantee to every State in this Union a Republican Form of Government." That second one is generally thought to mean that the Federal government must keep the states at least somewhat democratic.
That constitutional provision applies to the state government structure, not electoral votes. The framers did not support popular vote for president; thus, the electoral college.
No states chose electors using popular votes in our first few presidential elections, so guaranteeing a republican form of government did not require a popular vote for electors in the views of the federal and state officials at the time.