I bought this to play chess on my Kindle 3G, and to my surprise it actually worked. It takes the form of a very short ebook, at the end of which is simply a weblink to a site where the chess game can be played. It's tempting to think that as such it would have been possible simply to go to the site and play without buying the book, but since it only cost me about 70p that's all very reasonable. Thus I'm pretty sure it would need a 3G/Wifi connection to work, which could be annoying.
My main complaint is that I keep winning. Ordinarily this is not a problem of course, but given that I beat the program several times in a row without really trying, and it frequently made inexplicably stupid moves, I sense this is not a particularly well written chess computer. I would say it's fine for beginners, or to while away a dull train journey while not really having to think, but if you want to play a good challenging game of chess, go elsewhere.
Or find yourself a human; there is a two-player mode, which I have not yet tried, but I imagine could be much more useful (an alternative to those awful magnetic travel chess sets).