If the Dominion is trying to unmake Mundus by rebuilding the Wheel (or whatever the hell they're doing) so that they can rise to godhood again, then will the race of man not ascend with them?

If I'm right, man and mer originated from the Old Ehlofney and the New Ehlofney respectively. The New Ehlofney somehow ended up on Tamriel and became the Mer. The Old Ehlofney roamed the world and became the Men. So technically man and mer are both from the Ehlofney. So would the races of man not ascend as well?

Also, what do Khajiit get out helping the Dominion? Will they not be 'unmade' as well?

i dont think it would matter if the other races ascended as well, its just that Man has to die in order for them to be able to ascend.

It's nowhere stated as a fact that the Thalmor want to unmake the world. It does make sense, because escaping Mundus is what all mer (except the Dunmer) want, but they don't go around advertising it. So noone outside their inner circles would actually know about it. The Khajiit follow the Thalmor because those claimed to have brought back the moons that had disappeared for two years and that are very important to the Khajiit culture and biology.
Also, if that really is their goal, then it includes completely wiping out mankind. Because returning to the Aurbis is useless if another Lorkhan comes along and puts them back into a new world, so they have to wipe out all traces of the Lorkhanic idea to achieve their goal.