How is 'artistry' defined for women's gymnastics?
It isn't. That's the problem. Which means it's up to judges to decide, and coaches and athletes have to try to predict what the judges will like and strive for this nebulous idea of artistry without any solid objective basis.
I've heard of judges deducting because they didn't like the choice of music, because the athlete wasn't sufficiently elegant getting onto/off of the floor, (despite the fact that they shouldn't be deducting for anything that happens outside of the routine itself), and other such absurdities.
To illustrate some of the problems this causes, let's think about gymnasts who are typically described as "elegant" and "artistic," versus gymnasts that are described as "powerful." Think about gymnasts who were always described as being very artistic. Nastia Liukin, Svetlana Khorkina, etc. With no exceptions that I'm aware of, elite gymnasts with a reputation for artistry always have very long, lean body types. They're also almost always white (perhaps occasionally Asian, but even this is rare.)
Thicker, stockier gymnasts like Shawn Johnson are rarely if ever described as "artistic," no matter how technically precise they may be. Black gymnasts are rarely if ever described as "artistic." This is just how it goes in gymnastics media, and how it has gone for as long as I can remember. It would be ludicrous to assume judges to be immune to these biases.
Whatever "artistry" might mean in the abstract, in practice it's an open door for judges to give or deduct points for little reason beyond "because they feel like it," which inevitably means that subconscious biases will affect scores.
And so you have leotards designed to make the athlete's legs look longer, or make their waists look narrower, and so on.
The sport would, in my opinion, be considerably better off if all judging criteria were objectively defined.
(I may end up splitting this post off into a separate thread depending on how responses go, because all this is only tangentially related to the OP)