What does leftover rendered chicken skin consist of?
Fried chicken skin (gribenes), what's left of the skin after you render off the fat (schmaltz), gets its crispiness from the skin's protein. However, there is still a lot of fat coating and within the skin. When you crunch into it, there is still a "juicy" mouthfeel of telltale greasiness. The protein provides structure, but carries plenty of fat with it.

Similar phenomenon can be observed with chicharróns and pork rinds (fried pig skin).