Unless the viewer knows the music, it is not likely they will know what story the skater is trying to tell, no matter what they do on the ice. And even if it is not related to the music, how are most going to know.
I know the basics of The Little Prince yet I still had a hard time following Nathalie and Fabian's free dance in 2014. If I didn't know the title of the music beforehand I would have been even more clueless
I think the only ones that are self explanatory are the really iconic ones like Swan Lake or Carmen (a few others too) which is probably why we get so many of them. Anything else and its up to individual interpretation and could be anything. I could make up my own story based on what I see even with the already supplied story line At least Evgenia is trying to skate something rather then just skating pretty or dramatic like so many of the others. It may not be totally successful but its a valiant effort