first off, welcome to the forums!!
As far as I know, interaction between NPCs will be increased since now a big thing in the FF13-2 is branching dialogue trees, where different choices in dialogue will change minor parts of the story.
The "Temporal Rifts" system is a puzzle similarly based from the Cloister of Trials from FFX. These puzzles exists between the time rifts in game and solving them can fix the problems that are in the different time eras.
As far as other minigames, SE really stepped it up in FF13-2. There will be a new city/casino of sorts called Serendipity which is very similar to Gold Saucer in a sense. Floating high above the Pulse, players can go there to play slot machine games, race chocobos, and more.
The towns will play a bigger part and will be revisited throughout the game, but to what extent I do not know, I don't think players will be spending a lot of time developing the story through them like in other rpgs.
but thats all I know. Hope to see you around the forums.
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