This is coming from someone who is just a casual fan of the Castlevania series, not a hardcore fan. I do emphasize with how hardcore fans feel about reboots though, being a hardcore fan of two series that have been rebooted, one good and one bad. With that said, I really enjoyed this game. It leaves a lot for improvement, but there's nothing that really breaks the game.
The combat is not as deep as an all out action game such as Devil May Cry, and is much closer in style to God of War, with emphasis on the circular chain whips. However, I enjoyed the combat system more than I did God of War, and it definitely feels like a step up from Lament of Innocence, which is the only other 3D Castlevania I've played. There's plenty of variety of moves by the end, and they never get too complex to pull off. Fights are appropriately challenging. There's a lot of platforming though, which can get rather tedious.
I thought the plot itself was fine, but told in a rather unclear way that probably takes another playthrough to understand. It felt more engaging than most of the other Castlevania games I've played. The focus is on Gabriel's humanity slowly degrading over the course of his quest. I won't spoil the end result, but I was satisfied with it. I never really felt that kind of depth from other Castlevania protagonists before this game, or at least not to that extent. Same goes for overall themes.
While it is mostly medieval setting, I actually feel that the environments have an interesting take on it. Aside from the first few levels, the forests and ruins feel a lot more ancient than the typical sort of fantasy setting, very pagan. While the world of death is an ugly brown, it's an other-worldly type of desolation that's not quite typical of an underworld. I really do like the art direction, helping to emphasize more of a European "folklore" aesthetic rather than the usual fantasy, high or low. This game is pretty much set in a time in which a fantasy world changes into one of horror.
It is true that this game probably isn't going to satisfy the very hardcore fans, but I think as a reboot it's fine and is a lot better than some other reboots. It is mostly a Castlevania in name only, but on its own merits its at the very least a decent game worth checking out. I give it a B, and I believe that the sequel will fix the issues this first game had.