The Spaniards conquered the Mayans & Aztecs by a bizarre cancatenation of historic coincidences, disease outbreaks, and extremely skilled diplomacy, not because their weapons were superior. One Mayan kingdom held out against the Spanish until post-1700.
Did the Aztecs & Mayans have siege? YES. They conquered walled cities all the time. Their siege tools and weapons were not onagers and trebuchets, but we didn't want to do a bunch of specialty weapons just for the Aztecs. So sue us.
Did the Aztecs & Mayans have swordsmen? YES. The obsidian-edged "sword" used by the meso-americans was a perfectly good weapon. It was able to slice through chain armor, cut off a horse's head in a single blow, and even after the obsidian blades were chipped and broken it made a fine mace. They were not as durable as metal swords, of course, but that's not everything.
If you want to go looking for historic inaccuracies in AoK there are hundreds of them. Every civ has gross inaccuracies and errors we chose to make in favor of playability.
Now to display your lack of knowledge of other mythologies:
You ask:
1. Chinese: Tell me one G-d and MU (EXCEPT FOR DRAGON)
They had a whole pantheon of gods. Wen-Chang, Xi Wang-Mu, the Jade Emperor, Ling-Guan, Mu Gong, Pang-Gu the primordial giant etc. etc. They have tons of Myth units too -- celestial tortoise, Phoenix, Ki-lin (the chinese version of the unicorn), and a wide variety of horse-headed demons, giants, monsters, and goblins.
2. Mesopotamian- A lot of G-ds but MUs?
They also had plenty of MUs. The scorpion man, which we stole for the Egyptians, is just one of them. There is also the Bull of Heaven, Basmu the giant multijawed snake, Alu the demon without legs ears or mouth, the monstrous Tiamat, and so forth.
3. Meso American- A lot of G-ds and maybe the Qetzalcoatl MU but we know ES guys and they may give them siege weaponry.
Get stuffed.
4. Israelite- Single G-d
Too controversial.