I’d say it looks like a layer of burlap, then cotton on top of that 3 or so layers, muslin if you want to hold the cotton down, then appears to be foam on top of that.
Hey Chris, I was just scrolling through the pics you had in that link you provided. That is a great idea using the heim joints for the center backrest hinge pins. I'm going to put that one to use in the future.
I use the same method as Gordon but I use a foam bun. They have a skin on one side and stiffens the seat and evens out the weight. Plus they are cheap.