I just finished watching the presentation with English subtitles that's been posted on YouTube.
I've gotta say, at first I was a little skeptical, mainly due to the name of the game giving off this sense that this isn't really a direct sequel to the previous two. That, and the fact that the images they were showing were kind of boring without any real context to them.
But now the title makes sense to me, and I'm really excited to see what they can do with this game. The focus is on Lightning, and thus she gets the main billing. Also, this is a new direction for Final Fantasy, as it seems like they are trying out a lot of new ideas (character customization, real-time battles that affect the passage of game time, etc.). Whether it turns into a mish-mash of different ideas with no coherence and no tie to the previous games, or a great experiment on Square Enix's part remains to be seen. But by not calling it XIII-3 they are implying that this is a different experience, one that we may never see again for a console Final Fantasy game, and certainly not in the main series.
I don't know how it'll turn out, it could flop tremendously, but my hopes are high. Plus, I'm excited to actually play as Lightning again!