I haven't watched the video, but I will say that I'm quite liking FFXIII-2 so far (I'm not terribly far yet). Though that's coming from someone who really liked FFXIII (the battle system and the leveling system were really good and the plot was coherent and mostly not crap (minus Hope and Sazh), I don't really ask for more from an RPG frankly).
The story is a bit weird due to the time travel, with some moments where I think "huh, guys, you already know that...", but overall it's fine.
The battle system is just as solid as it was in XIII, but with the added bonus of extra attacks from monsters as you fill up a meter (it works as a QTE-ish element, but it's actually well implemented since you have control of when you want to activate it), and the fact that you don't lose a battle if your leader dies (only if both leaders die, which makes sense).
The Paradigm system was changed a bit due to the use of monsters, here you only have 3 possible roles at a time in the third party position since you can only set 3 monsters in there at all, but I think it adds a bit of strategizing to your party building.
The leveling system was changed completely, and I think it's pretty good. You use CP to open the next "node" in the crystarium, each of which gives a level to one of your roles (which you choose, so you can decide which roles you want to be good). You learn abilities once any given role reaches a certain level, and reaching certain parts of the crystarium gives you a choice of bonuses (ATB boosts, stat boost, role boost, new roles, more capacity to equip accessories). It's pretty solid overall.
Overall it's very much like FFXIII, but there's a few really interesting modifications and it feels like a very good sequel. I think it's very solid, I'm loving it.
The only down point for now is the QTEs during boss battles, but they're better than in most other games that use QTEs (since the game tells you when to expect them and when they end), and you have actual in-game rewards for getting them right beyond the usual "you can advance through the game now". A bit annoying, but not game-breaking.