I think you'd like Oni, for the very fact that it is...

A game set in a Dystopic future staring an Asian woman highly skilled in acrobatics, martial arts and weaponry, who is betrayed by people she trusts and on the run from the city's Police force, part of which involves a chase across building tops. We find out about the tragedy surrounding the woman's parents through flashbacks, her father's life changed forever after his wife died tragically. An old man betrays the Police in order to protect the woman, and ends up being shot for it.  The game eventually leads to a brutal fight involving her only sibling.

Sound familiar?