On a sunny day, total solar energy hitting the top of the atmosphere gives about 1360 watts per square meter (source - top result from google, something something NASA). It takes about 4.184 joules to raise one ml of water by 1 degree celsius. Let's suppose that the "suitcase" proposed in the article has 1 square meter of space (a pretty large suitcase) and is able to capture 100 percent of solar energy (unreasonably effective). Then pure solar energy-wise, there is enough energy to raise 325 ml of water by one degree of celsius per second in a square meter. If the water is, say, at 16 degrees (the temperature of the ocean near me), in would take 84 seconds to bring 325 ml of water to boiling temperature. To transform boiling water to steam, each ml of water takes an additional 2257 joules. In 540 seconds, the 325 ml of water is now converted to steam.
In total, it has taken 624 seconds to steamify 325 ml of water (under very optimistic circumstances). Morally one could do this almost 6 times in an hour, giving approximately 2 litres of water per hour.
(Edit): Looking a bit closer, I see that the article's description of their work suggests that they recapture some of the energy from condensing the steam back into water. I didn't account for this. Even a moderate amount of recapture changes the math very favorably.
This makes me suspect that their claim of 4-6 liters per hour would require a rather large "suitcase"-sized device, but is within the ballpark of reason.