What material to use for the spine in the binding of a paperback book?
I have used both of these when I bound my hardcover books. I am unsure if either of these are what you have pictured though

Bookbinding cloth

Also known as book cloth or Japanese book cloth. These are paper backed materials, which make it good for applying adhesives, and usually are made special designs. I have use this for just the spine for flair and to make the material last longer (used for more books). 

Cheese cloth

This is easier to come by, since it is not exclusively a craft item , and works relatively well. These come in a variety of grades and the finer ones would be preferred for this task. 

Both of these should fit your criteria