The assertion in the article is that:

   Even in desert conditions, there exists some level of humidity that, with the right material, can be soaked up and squeezed out to produce clean drinking water. In recent years, scientists have developed a host of promising sponge-like materials for this “atmospheric water harvesting.”

The number returned by Google (for what that's worth) is:

  The Sahara Desert has an average relative humidity of 25 percent.

In the part of the world with driest air and least rainfall ... you could always melt the ice underfoot.

Imagine if future climate change caused legal disputes about neighbours drying the air too much before it gets to others.

This kind of tech always gets spun as "water harvesting for deserts" but somehow it never makes it to more efficient dehumidifiers.

They talked around something like that in the article "...who envisions a practical, household system..."

That made it sound like a (practical) dehumidifier, not a (futuristic) personal water harvester.

Sahara desert average air humidity is .. I think 25%?

As far as I know most air trap type humidity stuff works in the desert, just not as quickly as in, say, the jungle.