Comments of chapter undefined of Demiurge: A Poseidon self-insert in PJO from the POV of others(PJO SI)
Gods have Divine Authority over a Law of existence, they also Bleed Ichor which is Gold. Their parents are Gaea and Oranous(butchered his name. Names have power, and saying it will let beings of a certain power know they're being spoken about by mortals. They're only considered Goddesses to Roman's. Because the Elder Cyclops were not God's but monsters and they were children of Gaea and Oranous, same is said for the Giants they're parents are Gaea and Tartarus, but the Giants are not Gods even his they have powers like one.
It doesn't really answer though. Cyclops mythologically inherited the authorities of Gaia and Ouranos and this is why they could create wonders. They are technically smith gods like Hephaestus. If we follow your definition of a god, Hypnos and Thanatos aren't gods, Nemesis isn't one. It was shown in canon that saying the name of Alcyoneus, a giant changed the world, and everything became darker. It was the same effect that happened when saying the name of Hades.