Hey, did you notice that every time Link swings his sword in the trailer, the icon for the Skyward Sword Girl flashes?
If the indeterminately gendered "bad guy" is indeed another sword, I find it interesting that he/she can teleport. If he/she can teleport, can Skyward Sword Girl teleport also? Maybe this is how Link gets from Skyloft to Hyrule. In any case, I sense some kind of connection between the sword girl and the girl guy, based on their similar skin tones and diamond patterns.
Some people have suggested that the "bad guy" could be an interloper. Didn't the interlopers get banished to the twilight realm and become the Twili? Well, the Twili can teleport too, only they use black squares instead of purple and yellow diamonds (and a square is like a diamond...). The Twili also have very pale skin. People have also noticed that Zant had a thing for diamonds. Perhaps these "sword people" are what the Twili used to be before they became as they were in Twilight Princess. In TP we saw that twilight can transform/corrupt things: Link turned into a wolf, the enemies got Tron lines, etc. .
...So there might very well be interlopers in this game! Whoo!
Hey, we might even get to see Midna as a Sword Person; Twilight Princess never specifies how old she is or how old Twili can get.
I can't wait to play this game!!!
EDIT: Ooooh, hey, if that guy/girl/thing on top of the statue really is of the same race as the Skyward Sword Girl, what if he is
somebody else's sword? Maybe that somebody else is the main bad guy.