As Travis Bickle, you use
guns, knives, baseball bats and any other weapons accrued from your passengers to take on New York City.
You win when the streets are completely scum-free. Estimated game-length? Ten years. Like a nastier Grand Theft Auto IV, basically.
In the scene where Travis complains about the scum, he doesn’t actually get out of the cab to do anything about it. You will.