> Their right handed writing was an artifact of that culture.

Sure. But that does not define a person as a right-handed writer. That's precisely why I wrote "individual's ABILITY to write with their right hand".

If you can't write with your left hand, because you never learned to do so, and you can with your right hand, you're a right handed writer. That's the only form of writing you can do.

Yes, the underlying handedness is independent of culture, but the actual ability is cultural.