Clearly lots of people have asked this question!
This site seems to have the answer.
From your link, are they saying that 'We Can Work It Out', 'Day Tripper', 'Help!', 'Ticket To Ride' and 'I Feel Fine' are all the first music video, or is there one of them that is the first? I also thought I saw on another source "Hello Goodbye." Do you know if there is specifically one answer?
That site isn't clear which was the first. You might Google each of those songs to see what you find.
It was A Hard Day's Night, first aired taped song by the Beetles, on the Ed Sullivan Show, May 24, 1964.
I'm a little confused now... you say that it a Hard Day's Night, but I've seen other sources that says is was "We Can Work it Out/Day Tripper."
Ok, we are in definitions.
Hard Days' Night was released as a tape, aired on the Ed Sullivan Show, in May, 1964
We can work it out was released as a picture disk December 3, 1965
You decide what you mean as a "video"