Triple cooked chips: Removing moisture by cooling

The matter here is much more complex than simple "drying out". Starch physics is complicated stuff, and I don't know it in all details, but here is the rough picture.

Starch starts out in tiny granules in the plant. When it is soaked in water and then heated, there is a temperature at which it rapidly turns from a starch suspension (if you had free starch) to a colloid (starch gelatinization). The theory is that these tiny granules burst, but I don't remember if it is proven yet.

At that point, the starch colloid is at its softest. It starts slowly losing water and recrystalizing (starch retrogradation). You can best see it in standard French bread - if you try cutting into it in the first hour after coming out of the oven, you get squished gluey crumb. After that it is soft like cotton for several hours to a day, but gets drier and harder. On the next day, it is already quite dry, and soon after it becomes stone hard.

Just like the gelatinization process, the retrogradation is also temperature dependent. And it happens to work quickest at fridge temperatures. It is slower at warm temperature, and stops when frozen.

So, your goal is not simple dehydration, and other dehydration methods will not really help you much here. You have to stick with what works, and that's temperatures just above freezing.

There are a lot of things going on to change the starches in the potatoes besides drying too; see rumtscho's answer for more on that. However, the drying matters as well, and these are indeed good methods of drying.

Refrigerators and freezers are notoriously good at drying things out. You might've noticed food drying out in your fridge if it wasn't well-covered, and freezer burn is a huge deal.

The air inside fridges and freezers is kept pretty dry, and it's circulating, pretty much ideal conditions for drying. Freezers really need to be pretty dry, since they're trying to prevent frost formation. But fridges are dry too too: the air is only a little above freezing, and the cooling coils are below freezing, so moisture is drawn out. Either way, it's still air-drying, just at a cool temperature.

Hot air is also good at drying things out, but I don't think you actually want the drying stage to further cook your food. Leaving it at warm room temperature with a fan would dry it pretty well too, but then you'd have a food safety issue.

The main alternative would presumably be a dehydrator, running at a bit over 140F, thus keeping things safe while avoiding further cooking. But that wouldn't accomplish the same changes in the starch, and that's not something most people have, so the fridge/freezer seems to make a lot of sense as a common, effective method.