Seems extremely flimy-flammy, but they do offer a money back guarantee if you don't jump 10 - 20 points on a standardized test.
IQ Tests are highly trainable, but the gains don't tend to transfer to other IQ tests, so it's not very surprising that they claim that they can improve your scores on some standardized tests. I remember Gwern has written a bunch about this, but can't easily find it right now. Here is one paper that I remember that covers some of this.
It sounds like they do an advanced form of Dual-N-Back. Gwern's analysis suggests that the reported effects of Dual-N-Back don't reproduce and are artifacts.
Gee, if I do the training twice, can I get 20 - 40 points?
IQs are defined on a normal curve, and a standard deviation is 15 or 16 points, about the midpoint of the promised 10 to 20 point gain. A 1-sigma gain (for any reason) becomes statistically less and less plausible as one moves to the right of the curve. Based on the education levels in the user survey, Less Wrong readers are already a lot smarter than average. So, for us, probably not. For Joe Average, maybe so.