Did the writers/directors bother to read the Constitution? (Spoilers)

Yes but we that amendment is in place in case no one gets a majority of the electoral votes after the votes have been verified. The voting machines had a glitch and therefore, those states votes cannot technically be valid after the glitch is discovered.

The whole section reads as "The person having the greatest Number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President"

The problem with your statement is that the electors that were sent were not valid because the election results were proven to be false. Like I said, there is nothing in the Constitution that covers this situation. This Amendment was added because the elections of 1796 and 1800 didn't have anyone win enough of the electoral votes, mainly because at that time there was only an election for President with the winner being President and the person in second place being Vice-President. They wouldn't, as you suggest, just toss out the votes of people in 13 states.