I think FT didn't intend to create some new fictional universe. What you get of FT is just a decadent and harsh setting/atmosphere, and the opportunity to use some strange vehicles and technologies.
Also, the hover vehicles intensify the feeling that bikes now belong to a different world and are 'precious'. The gangs represent not only a lifestyle, but also some kind of ideology.
Other than that, there is no 'mythology' needed to create around it. There is no purpose to fix it down to a particular year, or any nuclear wars or politic upheavals that might have taken place and resulted in what you see. There might be even a lunar base in the FT world, but nobody would seem to care about it.
I really love maps, timelines, prequels and expanded universes, but sometimes, vagueness can be more immersive