There are no diagonals in this test cart.
There -are- diagonals in this test cart... but it only registers buttons presses from an emulator while in the 4 player multi tap test screen...
I'm on my phone and can't see the videos right now, but my point was that the NES collects input by polling the registers at $4016 and $4017, then storing the result in RAM. The result is 8 bits (up, down, left, right, A, B, Start, Select), hence there is no distinct diagonal.
However, I assume what you're referring to is that the diagnostic test doesn't ask you to push two directions at once to see if it can be done, which would be testing the physical attributes of the pad rather than the circuit connection. I suppose you can allow for that in the software (the test) but maybe I just misunderstood what you meant.
I agree that diagonals on some pads can be tricky (such as trying to do them in Dead Or Alive 5 on a 360 D-pad) so being able to test it would be useful.