I think the main idea is this:
The Akaviri are the humans populating the majority of Akavir, and the Tsaesci are the ruling race that essentially assimilated, dominated or enslaved the Akaviri. They did not literally "eat" them to extinction at any point, as there's still Akaviri people presumably living in Tamriel (particularly Cyrodiil, as the Fighter's Guild was initially only composed of Akaviri men, not to mention the Blades and their whole deal), though they may be an ethnically and culturally diluted minority.
The Tsaesci themselves are, thus, not "human". Where exactly on the scale they are is hard to pinpoint, maybe they're antropomorphic like the Argonians, but with more snake-like features and different body morphology. Maybe they're closer to the Lamia and Naga fantasy archetype of a being whose lower half is that of a snake, but their top half is human or human-like. They could also be literal snakes, but I'd assume they at least have hands of some sort, as they don't weild their dai-katanas with their mouths! Personally, and thinking pragmatically, I would say the first option is more accurate: they're an anthropomorphic race with strikingly different features, namely snake-like features, long lifespans, and possibly vampiric and a larger/taller size than the average men and mer. They could have just a tail, and no legs to speak of, while still retaining that look on the rest of their bodies. This would also be the most logical option considering Bethesda may feature them in future games, and they would have an easier time modelling, rigging, animating, etc., something vaguely human rather than big snakes, and also would have a much more interesting race than yet another "plain" human variant.