This argument presumes that you cannot sleep on your own in a relaxed state and need assistance to fall asleep.
In order for software to cause sleep it would have to inititate the stages of sleep in a fashion beyond your control. By cause I mean 'to render you unconscious', as per the Hollywood image of someone being chloroformed, or the very real use of anesthesia at the doctor's office. Putting an individual to sleep in this manner should be as automatic as a drug, but still step by step, as the process should naturally occur. I will presume here that no other method of establishing sleep is being used (especially pharmaceutical at this point).
The software should, if successful in initiating sleep, cause your brain to produce High Amplitude Theta Waves. According to about.com's article on the stages of sleep, this is stage 1. If this does not happen because of the software alone, then it did not cause Stage 1 Sleep. "Initiating" in this sense is a forceful start of the Sleep cycle that allows the body to take over after it "gets the ball rolling". There are also no claims or explanations about how the product protects the Sleep Cycle from being interrupted.
There is a comment on the page linked in the product review provided where a commenter claims to be a light sleeper and cannot fall asleep with this Software active. This is clearly an instance of the Software being unable to fulfill what it was deisgned for. I can definitely say, this product does not work for everyone, but may remove stress in some or most cases, if the comment is accurate. The Wired review article also linked in your question states something very similar.
Sara Mednick, a sleep researcher at the Salk Institute and the author of Take a Nap, Change Your Life, says there's no hard science proving that pzizz and programs like it actually improve sleep. But the promise of a planned, computer-controlled, 30-minute nap to refresh the system is alluring to the modern psyche.
Verdict: It's all in your head. It may trick you into sleeping, but you're really falling asleep on your own. You could possibly achieve the same sleeping success by listening to an extremely boring lecture, or sitting on a comfy couch after eating a large meal, but there's nothing in the product listed that would cause you to sleep directly. This product only assists in relaxing the listenener. This software is more accurately a "Stress Removal Aid" and not a "Sleep Aid". If you fall asleep to the product linked above, there's a good chance that you could have fallen asleep on your own.