Well.. The important aspects for me are the turn based movement, and the strategy involved in when and how to use the resources you have to get out of super hard situations. E.g. In shiren for ds when I reached the last boss I managed to use my available items to turn it into a mouse and kill it in one hit.Uh. Levels are random, drops are random, nothing carries over run to run, and death is permanent. Maybe I'm misusing the word roguelike but I thought those were the necessary characteristics.
Now that you mention the characteristics, and that I've been playing the game for an hour I could say it's arcade/roguelike, but that's a topic for another discussion. Let's just leave it as a great game.