As a non-dancer, but a photographer of the dance, I have found this to be a very interesting line to follow. Initially I would have thought that perhaps ballet is a "sport", because of the very athletic ability I see in the dancers. It is a good point that there is no "scoring" per se, however, would not the "enjoyment level" or "quality level" of the ballet as perceived by the viewer actually be a type of "score"? Certainly the choreographer is very aware of the quality level of the participants in "his(her) dance". And, I also suspect that in reality each of the dancers is very aware of the competition between each other (in the corps) or with previous principals that have done the piece.
In my mind, I also find it interesting to compare the ballet to womens' gymnastics. In gymnastics, although in many aspects quite different, in my opinion there is both art AND scoring, and thus would be considered a sport. However, in photographing both gymnastics and ballet, I find the two types of resulting images very similar, especially if I take the gymnastics photos in the studio. In fact, I often use the same type of lighting to take studio photographs of ballet dancers and of gymnasts.
An interesting topic... but in the end, does it really matter? There is no question that ballet is an art. Cannot it be a sport also, if it makes someone happy to think of it so?
donb