To quote H. L. Mencken, "No one ever went broke underestimating the intelligence of the American people".
Mind you, I can see how this makes sense from a business perspective. When you're entering an already crowded market you need a gimmick that is going to set you apart from the competition, and selling pseudoscience to the scientifically illiterate is one of the tried and true marketing strategies of our age. All many people know about DNA is that the supersleuths on CSI use it to solve crimes because it's great for identifying people. Why wouldn't you use it to identify a mate? It's all very scientific, and as CSI teaches us every week, science always gets the right person!
Scientifically, it's nonsense. For starters there is the fact that human behavior is determined by both genetic and environmental factors, but our understanding of how the two interact is still very rudimentary. Then too there is the problem that in general there is no simple one to one correlation between genes and expressed traits (i.e. you can't tell, just by looking at someone's DNA whether they're going to left or right handed, let alone whether they're going to be a great violinist or have an IQ of 140). The function of large sections of the human genome is unknown, and our understanding of the regulatory sequences that determine gene expression still sketchy. In short, you can tell remarkably little about somebody simply from examining their DNA.
So what is comparing two peoples' DNA going to tell you? Well let's put it this way: loosely speaking, humans share about 96% of our genome with our closest living relative, the chimpanzee. If that sounds like a match made in heaven to you then DNA dating services are definitely the way go! :)