I find it interesting that the poster of the video decided to title his video "Summer Glau dancing" and not "Summer Glau fighting"; indeed, this is what makes her performance in Serenity so special, enjoyable and addictive (thanks Joss Whedon).
In order to illlustrate Summer Glau's unique contribution, here's a video of River's fighting rehearsal by a woman who is a martial arts experts; the fighing itself is ok and would be great in an action B-movie but Summer Glau's own interpretation is what makes it so special and why theses fighting scenes contributed to make of River an iconic character.
Well, it fits perfectly obviously, those scenes aren't only about a badass girl who beats up a bunch of guys but about a girl who does it with unimaginable grace and beauty. I always loved how Summer utilizes her ballerina background in her acting( not just here), it makes a beautiful synergy and makes her work truly artistic.
And the devotion and sacrifice she showed just so she can do these scenes even if she didn't necessarily had to made me absolutely confident in that Summer shouldn't be viewed as a simple entertainer who just entertains people but she is an artist whose works are like gifts from a great person to the audience.
The same devotion, art and effort shows every time she is onscreen BTW.
It's interesting that Summer says she can't dance anymore because of that foot injury, but she still seems pretty light on her feet in that one video.
Dunno, maybe hardcore ballet dancing still puts a lot more strain on her feet than the fight scenes or casual dancing or the brief ballet steps in TSCC.
I think there is a video somewhere about one of Summers dancer era dancing performances where she does insane things, surpassing even the fights.