Kiai is probably just the Tsaesci word for Thu'um (to my knowledge, both the dragon word "Thu'um" and japanese "kiai" translate to "Spirit Shout." I assume "eating the dragons" refers to Akaviri Dragonborn and eating men is vampirism, but it is a good call on the serpent/dragon-to-Lorkhan/Akatosh symbolism.
So while I don't think you're quite 100% right, it is food for thought.