Several links for this video indicate that it was produced in 1899, although the dialogue by the narrator implies a date of "1913." The dance is in the style of "Butterfly Girl" Loïe Fuller, who used billowing skirts to create a serpentine dance for the Follies-Bergere; interestingly she is reported to have used multicolored and changing lights to illuminate her skirts during the performance - the effect that this video presumably is trying to recreate.
YouTube link, via Kottke.
Why not play it back at whatever speed makes it look natural? No one watching it cares about fps; it's just distracting to have it play back unnaturally fast. Viewers have an intuitive sense of how things "ought" to naturally look, in terms of gravity and momentum and such, and it's the distortion of that that makes it disconcerting to watch.
I don't think it would be terribly difficult to get "close enough" to natural speed, at least so it wouldn't draw attention to itself. But then I've never tried, so maybe I'm wrong.
Unfortunately, nobody seems agree what the majority of silent films should be played back at, since there was no hard standard for several decades.