It's not a part of the story. It's a side-activity. A competitive type of PvP, for points or whatever system they choose to go with. Similarly, Ballista and Brenner were PvP type activities in FFXI that had no impact at all on the main game, and had no bearing on the storyline. It's just content for people to do who enjoy that kind of thing.
Nah. It's not going to become a PvP MMO on that scale. That much has been said already.
Here's a bit about the PvP from an interview with Yoshi-P:
Q: What about PvP?
A: There will not be open PvP/ PK, and both players must mutually agree to a PvP match. Final Fantasy XIV will be the first game in the franchise to have a “meaningful” PvP system, hence I urge players to try it out.
Q: Is it fair to say the PvP in Final Fantasy XIV is somewhat similar to World of Warcraft’s?
A: We will have a PvP arena, which is similar to the one found in World of Warcraft. Our PvP team members played many matches in World of Warcraft. Personally, I am a player of Dark Age of Camelot, a PvP-centric MMO.
-Source
I personally kind of "cringe" when ever I see a developer make a claim of how their MMO will "be the first" to do something, as it's seldom true, and too often way off-mark. What exactly do they mean by "meaningful", I don't know... I hope it's not in a sense where PvP rewards will somehow effect the main storyline and other non-PvP gameplay.
I'm already concerned about another quote:
“ We will have a strong in-game guide, making sure players know where to go and what activities are there to do once they enter a new map.”"
I really... really.. really hope that doesn't translate into "copious amounts of hand-holding, where the player never has to figure anything out for them self and exploration is never required to discover new places/things, because everything is pointed/spelled out for them."
Fingers crossed that's not the case.