how much space would one need to generate enough water for say, an average household in South Korea?

Alright, here are some "back of the envelope" calculations based on the information available. I hope I don't screw anything up, and please ignore my utter disrespect for significant figures.

The Mayo Clinical says that the average person needs about 2.7-3.7 liters of water per day. Normally, this comes from both food and beverage, so how much of that you actually need to drink is going to vary depending on your diet, but let's assume worst-case scenario, where all of your water comes from this device.

Given the stated output, and the fact that water conveniently has a density of 1kg/L, it seems that you'd need anywhere from 9-18kg (20-40lbs) of MOF to produce enough water for one person per day if this was your only source.

(1kg MOF/0.285kg water * 1kg water/1L water * 2.7L water/person = 9.5kg MOF/person)

(1kg MOF/0.210kg water * 1kg water/1L water * 3.7L water/person = 17.6kg MOF/person)

ArcGIS says the average household in South Korea is 2.4 people, so now we're at 22.8-42.2kg (50-93lbs) of MOF to meet the water requirements.

I have no idea what the density of MOF is, so I don't know how much space this would take up. Metals vary significantly in density, but we can look at Aluminum (2600kg/m^3) and Lead (11,300kg/m^3) to get some idea of range.

22.8kg * 1m^3/2600kg = 0.00877m^3

22.8kg * 1m^3/11,300kg = 0.0020m^3

42.2kg * 1m^3/2600kg = 0.0162m^3

42.2kg * 1m^3/11,300kg = 0.0037m^3

I'm struggling to come up with "real world" equivalents to help you visualize the volumes. The smallest one is a sphere about 16cm (6.3in) in diameter. The largest one is a sphere about 31cm (12.2in) in diameter.

Obviously, the device wouldn't be a sphere, and it wouldn't be made of just MOF. The diagram showed a tube of MOF wafers surrounded by a container, but that should give you a very basic idea of the materials required. Again, this is all assuming I didn't make any mistakes, which feels like a bold assumption at this point.

It sounds to me like it's pretty similar to how home oxygen concentrators work, but with an MOF instead of a zeolite, and driving out the adsorbed material via increased temperature rather than decreased pressure. MOFs are pretty comparable to zeolite in cost, and both can be used as molecular sieves, as in this case. Maybe you can find a video on oxygen concentrators that would help you understand it?

One difference here is that in the oxygen concentrator, the output product is the air, but with the nitrogen sequestered out; here, the output product is the water sequestered from the air. But this leads me to think that maybe this tech could also actually be used for air dehumidification, which could drive down the energy use of air conditioners. That could be another big win, since air conditioning is a major use of fossil fuel energy and contributes significantly to climate change, which is part of what's driving the drinking water shortages in the first place.