The ribbed spider web is a needle weaving stitch. During the development stage of my Snowmen Nestled in Spruce Trees design I tried the ribbed spider web two ways: the first with the fabric removed for open work (left photo below) and the other way with leaving the fabric threads uncut and not removed (right photo below).
I liked how the (right one) with the non-openwork looked with the red fabric threads showing behind the ribbed spider web stitch and also that the fabric held or pushed the worked spider web stitch up to be more dimensional.
To start the ribbed spider web stitch, create eight spokes (four long stitches). Two stitches (diagonal from corner to corner) and two stitches (center to center). Once you have completed the 8 spokes (4 stitches) you bring the needle up at the center fabric hole (the red dot).
Above is for working the ribbed spider web stitch above fabric. If you decide to do openwork (snip away the fabric inside of the Kloster block) then you get your thread into the center starting position by weaving it up one of the 8 spokes.
Back view below was taken after I brought the needle through the center hole to the front of the fabric.
You can weave the ribbed spider web going clockwise or counterclockwise. Whichever way you work the first ribbed spider web stitch, I suggest you do the same for the others within the design. I went counterclockwise on my first one and continued to do so for the others.
Top left photo shows the stitching thread coming up through the center (red dot) fabric hole. The needle is under the first two spokes. This is how you weave, needle under two spokes, pull through, and the loop will be formed around the right (if working counterclockwise) spoke of the two spokes.
Middle photo I am nearly finished weaving the spokes. With the four diagonal spokes being slightly longer than the other four spokes, I do a double wrap around the diagonal spokes as I go around the last time.
In the left bottom photo I am finished with weaving and I am stabbing the needle through to the back via the same fabric hole used by the spoke. Right bottom photo is the completed ribbed spider web stitch.
Photo of completed corner: