Is is possible to make popped potatoes?

The reason popcorn can be popped is that they have a water-impermeable hull, which contains the pressure of the steam created inside the kernel as it is heated, until it passes a critical point. When that happens, the steam explodes out, breaking the hull, and creating the popcorn. Some of the other puffed products are more complex, as the link you have already found shows.

Potatoes do not have a water impermeable skin, and so cannot be puffed in the same manner as popcorn.

There is a dish—sometimes called puffed potatoes—where the steam inside fried potato pieces is used to puff them up, but it will not be similar in texture to puffed grain. See this recipe, for example. They will be more akin to fluffy french fries (or chips, as they say in Britain).

There is another dish called puffed potatoes, which are essentially a choux paste with potatoes that are baked or deep fried. They are a great dish, but are a different type of thing entirely. See this recipe from the great Jacques Pepin.

The process for making most puffed products (except popcorn, which SAJ14SAJ has explained) isn't something you can do easily at home. As the link you included says, the grains are placed under high pressure with steam, then the pressure is suddenly released. This takes some specialized equipment. You can get the pressure and steam part at home with a pressure cooker, but they're designed to never release the pressure quickly, so you can't actually pop anything.

So should you have the right equipment, you can make puffed potato products. The example I've seen is Popchips. They're made with a similar process, popping something made from potato flour under high pressure. I'm sure there are other examples out there, but they're all going to be things you can't really do at home.

All this said, I do wonder if there's a way you can do something like muri (Indian puffed rice) except with globs of potato starch. It's still not an easy task, though. The rice is tossed into a sand-filled pot or oven; the sand holds enough heat to rapidly heat the rice so that the escaping steam puffs it. My guess would be that if you can get bits of potato-stuff to about the consistency of the soaked rice, it'd work, since both rice and potatoes work with the industrial process. But it's still an ambitious project to try at home. Perhaps some of our Indian users could provide some more advice!

To puff starches you have to cook them in water until very soft, then dry them completely and after that you can deep fry and puff them. I have not tried this with potatoes, only with pasta where it does work nicely. And you can do the same thing with proteins like bacon rind - just find a recipe for chicharrones (sp?).

If you have a dehydrator you can try to cook potato slices, dehydrate and then deep fry them. Without dehydrator the potatoes might go bad before they dry out. The puffing usually also works in the microwave, but without fat the potato is probably bland. And make sure to tell us the result!

PS: ever tried to put parmesan rind (well dried out) into your microwave?