Ooohooohooh, while it is possible it is woven with that texture you can buy a crepe georgette, preferably rayon or silk, cut it in to strips, sew it back together with a seam allowance of about 1/2" then wash the heck out of it. I have fabric that goes like this in a wash.
On closer inspection it does look like it may well have been done this way, the base fabric would be self striped (sheer and semi sheer) and then when sewn back together the stripes were alternated so there is a subtle checker pattern in the background.