Kat was actually pretty thoroughly explained in DmC. She was abused (hint of sexual abuse) by her foster father, who was a demon, and she would escape to Limbo to get away from her physical body to not feel any pain whenever this happened (she called it the nightmares). Vergil found out that she had this ability and decided to show her how to control it better, later helping her kill her foster father.
The thing I like about DmC and its story is that they don't straight out tell you everything that happened in detail but they give you the general idea so you can build off of it. This was non-existent in past DMCs, because you only knew about the events that happened within the game and that was it. In DMC1 you do get a bit of a flashback when you take down Vergil for the last time, but that's it. In DMC3, you have no flippin' clue how Dante's life had been until that point.... hell, he could have gone to Brazil, had a baby there with a random woman, gotten back to his shop, taken a shower, and BAM! the game starts. DMC4 does the same with Nero and his devil arm, as well as not showing how Kyrie and Nero's relationship built up (once the game start, they already loved each other).
Back on the gameplay topic though, it may not be as in-depth as DMC3/4 but the more I play the game, the more I realize that there are some crazy stuff that you can pull off and they are at DMC-level hard to do. The game is waaay too new to be judging it just yet.
And also, nice stuff Chaser! I watched your videos and it was a lot of fun watching a pro hammering the game, even though it was your first playthrough and obviously you were still getting used to the new weapons and stuff, you still did pretty well. That helm breaker cancel though... why can't I do it properly!? D:< Once I get that down I would have so many new doors open for me.