The examples shown look very fragile, and easily damaged.

Wall and ceiling cooling has been around for a long time. These two companies offer products that look spookily like those shown in the picture: https://clina.de/en and https://www.beka-klima.de/

Yeah, but I WANT the air dehumidified! If you lived in the sort of climate I do then you would too.

Heat is not "drawn" from hot surfaces; it radiates regardless of the temperature of surfaces nearby. What this system is doing is reducing thermal energy being radiated from the walls, which adds to the thermal energy a person acquires from conduction from warm air. A warm wall tailored to selectively radiate less energy in the IR band might feel just as cold as this chilled wall.

If this system makes people feel more comfortable at lower energy cost, in at least some environments (dry?), then it has potential, even if their description of physics is wrong.

How is this innovative? Lower than ambient water running through walls?! It would be a nice feature for outdoor events where the heat isn't from the sun. Give me a Radiant Barrier shade and a fan.
I also live in hot humid climate.

Since cooling is in essence removing energy, air conditioning should be a an energy producing endeavor.

Using radiant heat transfer looks cool in theory, but, If the air is humid, like along the Texas coast that chilled wall will not work outside. Cool water will be draining off the wall in large quantities... like it does on the outside of my windows each morning here near Galveston. The first task of a home or office building air conditioner is to lower the humidity to stop the mold and other scum. Then the cool air then makes it comfortable to live in the space.

The “energy efficient” electric radiant heat popular in the 1970s turned out to be pretty much a farce, foisted off on us mostly through huge subsidies from power companies. They often provided very poor heating at a very high energy cost. Add to that the need to avoid all the wiring -in this case plumbing, and any residential demand for this will self extinguish. It may very well find a market in the specialized applications mentioned in the article.

What! I can not hang up my pictures on the wall? No shelving? Can you even paint it?

Modern air conditioners and HVAC systems are not "notoriously inefficient." Their high efficiency is due to effective use of phase change in refrigerants and also motor efficiency improvements. We just need to power our AC with renewable energy.