Khajitts were described as a people with animal markings on their faces and Argonians were a `swmap people`...
I think "people" here means "tribe", "group sharing a culture", not actually "humans".
I can't see in-game descriptions now, but from UESP (Daggerfall article):
You are part of a highly-evolved race of reptilesSo no humans here. However...
You are part of a tawny-skinned people, extremely hardy, intelligent, and agile. Many Khajiit have taken to painting their faces to more resemble their legendary feline cousins, the predatory cats that hunt the great desert.Nothing at all about being a cat. Actually, this description suggests they're humans who try to resemble cats. This is further proved by their in-game looks: no fur, in Arena they didn't even have a tail!
So Argonians were they way they are now, but Khajiit were humans who later miraculously grew fur, whiskers and learned to see in the dark - because apparently they were more interesting as cat-people than yet another human race

It's funny that Khajiit are actually cousins to Bosmer - they were both created from the Forest People, some transformed by Azura and some by Y'ffre.
Even the lore tells us there was a time when Khajiit weren't cats
