To boil water you've got to add the thermal heat of vapourisation to water, 540 calories/g, or about 2 kJ/g.
To condense water you've got to remove that same quantity of heat. Granted that heat pumps are more efficient than adding pure heat, you're still looking at expending somewhere between 10--20% of the energy removed.
Energy usage also varies with the relative humidity and ambient tempuerature. Remember that both the lower the relative humidity and the lower the ambient temperature the lower the amount of water (absolute humidity) in the air. Dehumidifiers work best when handling hot, humid air, which is not typically where water is in short supply in the first place. Attempting to dehumidify cool dry air, say, in a high-altitude desert, will be exceptionally energy intensive and produce very little output water.
The condensation traps and nets mentioned in TFA work best in very-high-humidity environments. This can be useful, but again the total gains are limited, and the process remains the "un-boiling water" problem.
Dehumidifiers are one of the most energy intensive way to get water and if you live in a very humid region, well you already have water.
And yeah, there's energy input, but it comes from the sun and no one has to pay anything for it.