Of course it is an RPG. Just because it isn't your stereotypical RPG doesn't mean it isn't one. Why so many people have to try and weed things out because it's not your "perfect" example is silly. Funny how on the other side they complain if something is too like the "perfect" example as well. Hypocritical discussion I will never understand.
Whenever discussing things like this, I always go to RE4. RE4 is a survival horror game. It has shooting elements, it has adventure elements, it has puzzle elements, and even some small platforming elements in it. Hell it has a lot of things in it. But in the end it is a survival horror. The first ever in the series to be a cinematic one and more action packed but still a survival horror. It fits the mold in more ways than one and it is the dominant genre in it... but just because it's not like the traditional survival horror games doesn't mean it is excluded.
I think that same argument can easily be used for FF13 here as well.