I've just played it for a couple of minutes.
It's definitely an RPG. It might be a fullblown monster raising type game or more straightforward, but either way you control monsters (I'm not sure if you get a full party, or it's just one at a time) and they do the fighting.
See that big octogonal shape in the screenshot above? It pops up, and you press different directions (which visually creates a "shape" of connected pipes) then press the A button to execute an attack. Different shapes do different attacks. Kind of like the Xenogears or Legend of Legaia systems. Although it's turn based, the faster you input a move, the more damage it does. Once I finished that first fight, I figured out how to get a list of that character's attacks (and the character's stats). It looks like a couple are hidden, because it doesn't list the button presses for them. Or they're unlocked later.
I'm kind of hoping for an English release (however unlikely), because it looks like it'd be fun if I could understand what I was doing (or supposed to be doing). I wouldn't play completely through a game with this much dialogue in Japanese.
I'm not sure what the card that pops up on the official website (listed in the NFO) is about. Maybe it comes with the game, which may be based on some sort of collectable card game (though it doesn't play like one).