Okay, I'm interested. Looking at this one on Amazon:
Amazon.com: Char-Broil The Big Easy Oil-Less Infrared Turkey Fryer: Patio, Lawn & Garden
...it appears to be a specialized form of high temperature roaster. I suppose calling it a "fryer" can be forgiven, since the intended finished product is similar, but only for some forms of food. But it's billed as a "turkey fryer," so that's okay by me. If they had called it a "roaster," they would have missed their target market. (The bold use of the term "infrared" is sort of lame.)
It appears to be a tubular chamber with a surrounding catalytic propane element. They say the mesh lid is to reflect some of the "infrared" and to let hot air out. I'll buy that, it not a baker. So, why do we fry? Because oil can get a lot hotter than water. And because oil can surround the food, which matter a lot with, say, French fries, but perhaps not so much with turkey, since turkey is close to being a solid lump of meat. So, they're hitting the turkey with intense radiated heat. Different from the conductive heat of frying, but should work. So, as I said, a specialized roaster, and isn't that ultimately what frying is, a "roaster" that equally treats all sides of the food?
If I was inclined toward turkey frying (which I'm not), I'd consider this one, if only because it avoids the mess, cost and hazards of oil.