Neat idea for a game just hit me while typing up a page on Arcana Wiki about Orthogenesis, a discredited alternative to Darwinian evolution. Orthogenesis proposes linear evolution, instead of branching, so that no two species share a common ancestor. It's kinda silly.
But let's, for the sake of gaming, take it as true. You could run a game with a very limited gene pool, just a few dozen species fighting for survival. Player Characters might be reincarnated, or you just might play an entire species at a time. Point being, each PC is a different species. After every major plot point, the time line is advanced by 30,000 to a million years. When this happens, you spend your experience points evolving your species. I suspect this is going to need a competitive structure - defeating other players in the short term gets you the points to evolve in the future. Eventually, though, the divide between PCs would get pretty big, at which point the GM invokes an external threat to even the playing field (or just hide the difference). Or, perhaps as you evolve to fill niches, your xp awards change. Yes, Mr T-Rex gets points for eating me, but as an r-Strategist herbivore, I get points for hiding, eating plants, and having sex.
At the beginning of the campaign, there's no culture, or language, or tool-use. Those are things you can choose to evolve, along with gills, limbs, venom, camouflage, psychic powers, etc. Obviously, the game system would need to be pretty flexible, yet at the same time have defined options for adaptation.
Ooh, adaptation! How about, at the end of the story arc, you get to propose one evolution for each way you died. He keeps eating me, so I evolve poison and bright coloration in his visual range.