Honestly I don't believe that that "interlopers" story will play a role in the game. As far as I remember from TP it's a very old story from archaic Hyrule when the Triforce was still lying around and nothing really happened in the world. The Hyrule as seen in the trailer seems to be at much later and more developed stage. Plus it was just one single cutscene in TP, so we shouldn't overestimate the impact of said cutscene.
I guess Nintendo will do it as usually and by that I mean a whole new, totally unexpected story which might have little to do with the other Zelda games. Look, who would've thought of Termina, Majora when OoT was the newest game? Or who would've expected a flooded Hyrule before the release of the game? Or the whole Twili-centered story after that?
And I also don't think that it's Vaati because for me the pre-DS handheld games somehow don't fit in and are usually much more gimmick-y and free to do as they please/less restricted when it comes to storyline. I can't remember any console Zelda which made any reference to a pre-DS handheld title yet. Link's Awakening has practically no connection to anything else (because it takes place in a dream), the Oracle games take place in a totally different land than Hyrule which has no connections to it and references to older Zeldas seem totally random (we have the Mask Salesman there, Biggoron, Guru-Guru, Twinrova and many more but other than their names and appeareances they are totally unrelated to their Hyrule counterparts). It's similar with TMC, here too I think that people are overrating that one single line of text in the game where it says something about "Link's first adventure". This has no significance at all to me because it could be either a translation mistake, relating to the first adventure which
that very Link from the game is on or maybe Capcom even planned a sequel to TMC which would then have been the "second" adventure of
that Link.
Oh, and by the way the guy we see in the trailer reminded me a bit of Sephiroth when I first watched it
