If their goals are based on the metaphysics of imposing their spiritual beliefs on the cosmos, then they surely need to destroy any one who doesn't share their beliefs. IE, any one who isn't Thalmor.
Humans would be the first target because humans have been the most successful at imposing their beliefs, but I can't imagine it would be very long before they turn on the other non elven, and then the other elven, races.
Yes, this is why they're destined to fail. In the alternate-universe chance that the Thalmor destroy all humans and subjugate Tamriel, the longer time goes on, the more they'll wonder why they haven't ascended yet. Eventually they'll turn on the "lesser" elves for this reason. And when still ascension hasn't happened, they'll eventually turn on each other. Their principle is seen a lot in history, and it's always a prophecy. A self-fulfilling prophecy.
Really interesting stuff. Props to Bethesda.