Kai'sa is a lot like Kerrigan from Starcraft 2
I think what they were trying to do is make her look like Kerrigan from Starcraft 2. Here story is a lot like Kerrigan, has wing like weapons, in-tune with the Void, Changed by it, but still sexy somehow...
Here default skin look pretty much like Kerrigan after she came in contact with the Void (yes they call it the Void in Starcraft too) & "Evolved" into the "Queen of Blades". Her "Bullet Angel" skin looks like Kerrigan's "Queen of Ghosts" (Ghosts are government special ops) before she came in contact with the Void.
In the game Starcraft 2 you can change here abilities to give her a different play style & she would "Evolve" with new abilities. Some of her abilities are the same too. Kerrigan could go invisible & she had a dash move that did a good amount of damage.