Puzzle Quest Galactrix will be like, except that the DS one will look different, cost money, and last longer. Playing the thing will explain the concepts of the game a lot better than we can. Even the pre-demo instructions seemed complicated (and we've seen the game before), until we started playing, at which point we just got it immediately.
We wanted to complete the demo, so we could take in the entirety of the presentation before reporting it for you, but that's just not going to happen right now. In fact, we're going to go ahead and proclaim that it's impossible to beat General Tarn or whatever, and also that the game is cheating and it's totally not fair.