I remember that the dragons were originally the inhabitants of Akavir. The other guys that I can't spell are the ones that invaded Cyrodiil. I think you helped me work it out:
The dragons were inhabitants of Akavir, but got pwned by these weird serpent people.
The dragons then went to Cyrodiil and helped them defeat the weird serpent people from Akavir.
The Empire was then united under Reman Cyrodiil.
However, after the Oblivion crisis, the Empire disbanded (because of Martin's death)
This is mentioned in the video -
Their defeat was merely delay
Til the time after Oblivion opened
So therefore Skyrim had no connection to the Empire (or Cyrodiil) therefore, the dragons wouldn't be beefing with the wrong guys, yo.