I checked out their website last winter. I got the impression that the system is basically a ventilating fan placed at the lowest point in the home where, supposedly the heavy, humid air tends to congregate. It vents that humid air to the exterior of the house thus reducing the net humidity in the home. The air in the basement is also more likely to be musty than upstairs air so that when the basement air is expelled, so is the odor.
They do comment that it will increase your heating bill a bit, but not significantly.
I guess it could work; you are getting rid of the least desirable air in the building. Slightly cracking open a basement window might do the same job however, their system is set up to pull the air off the basement floor and duct it up and out.