Drinking water devoid of any minerals is not good for one's body. On the other hand water vapour can carry air borne contaminants particularly well, which might be another thing to watch out (although the after-filters provided) would probably do the job well.
It's called a dehumidifier. They've been around for years. Looks like this one simply added a water filter.
It looks like a highly sophisticated de-humidifier...a very cool product nonetheless.
I think I'd be interested to know what the effects of an industrial sized system like this could have on an area such as for mass irrigation. Is it possible to extract too much moisture out of the region?