It may not have been related to Final Fantasy.
But it will be now.
There will be a relationship between Youkai Watch, the characters, the weapons, etc and Final Fantasy.
This relationship will be undoubtedly developed and refined through dialogue and quests.
I very highly doubt the management will simply put these items / minions / FATEs into the world with absolutely zero explanation or lore.
There is no way.
Easter is not a part of FF Franchise either. Nor Christmas. Nor Valentine's day. Nor Halloween.
But it was added to the game.
I didn't participate in any of the seasonal events because they didn't interest me. But I did accept one of the quests once. There was a lengthy explanation about it.
They will be incorporated into the world through lore and story and a relationship will be built.
Santa Claus wasn't always related to Christmas. But he is now. And the world did not end.
Things change. It's okay.