Trudi Canavan wrote a series of books I think called the Age of 5 trilogy, which is about a war between two religious fundamentalist countries. Spoiler Alert and in that series the gods have their followers hunt down any immortals because the gods themselves were once immortals and any person who is powerful enough can figure out how to become immortal and any immortal strong in enough can become a god if they figure out how.
You could take that approach the gods in your game are living entities but the player go pursue the path to godhood but doing so will but them at the odds with the gods as they are greedy and jealous.
Oh man i love those books
But yeah, i was gonna suggest the same thing. Stargate SG-1 in season 8-10 did a similar thing. You had "gods" because people who worshipped them didn't understand what exactly they are. And they were ascended beings that once were ordinary people who found some kind of inner peace and understood the state of mind required to discard their mortal flesh and go to a higher state/plane of existance. So basically, they have all the characteristics of people (so you can make them be as black/white/grey as you want), but also have the power to influence mortals in some way (and you can decide what way that is).