AFAIK, Warframe isn't particularly based on any one mythology; a lot of the names come from Greek mythology, and there's definitely a little bit of Greek bias (perhaps because Greek and Roman myth is pretty common) in the imagery of the storylines and the Orokin, but there's a pretty heavy emphasis on having the whole thing flow out of this framework of mythology that makes the story truly epic.
It's a good game. I don't play it all that much, even with that said, but I definitely think that Warframe is one of those games that both treats players right and does a good job of being a fun game (they're not unrelated, mind you, but there are games that have the best intentions and fall flat).
This comment only makes me wanna play it harder, lol. good thing i'm already downloading it!