I don't see why Argonians don't get that +15 damage when using unarmed attacks like the Khajiit have.
Well they don't get that, but they do have increased unarmed damage.
http://www.uesp.net/wiki/Skyrim:Combat
According to that, Khajiit and Argonians have a base unarmed damage of 10, while all other races have a base of 4. Add Khajiit's claw bonus (which is supposedly 12 and not 15 as listed), and they have 22.
So Khajiit (22), Argonian (10), Others (4).
As for the lore, I'm 100% positive Khajiit have unarmed martial arts. It's even noted in Skyrim:
Spoiler In the Dark Brotherhood quest, Astrid's husband (Werewolf dude, I forgot his name) tells his guildmates a story about a contract he had to take out a Khajiit Monk who was trained in the arts of the Whispering Fang.
I'm not sure about other races though.