Just a little theory, but I have a feeling that Square is setting this one up to be a (very) loose prequel to FFVI.
First, we already know that the summons are called Espers, a name they haven't been called in any other FF besides VI.
Second, the story looks like it will be about a great war - one where magic is used wantonly, much like the War of the Magi 1000 years before the events of FFVI.
Third, the latest trailer posted at the official website describes it as "a story of a time when magic was commonplace." FFVI, unlike many other fantasy games, is about a world where magic is not commonplace.
I know Square has made many other references to previous games before, so I doubt that these references are anything more than superficial. Still, it's interesting to think about.