It's not that the original Final Fantasy XIV didn't have a real story — it's just there was so much extraneous crap separating the player from the narrative. When the original launched in 2010, the story unfolded sporadically between extended bouts of guildleve (repeatable quest) grinding.
Here there is a well-defined quest line. The player feels like some sort of legendary hero. Your character progresses smoothly from nameless newbie to potential legend in a natural (well, as natural as it gets) fashion.
With that in mind, this really is a trailer for a solo Final Fantasy game, hearkening back to the originals, in which a group of mysterious heroes rises to greatness to save the world. The only thing missing is the main character — that's where we come in.