How is the string attached to this clear piece of plastic?
As you've noted, the thread passes through holes in the plastic sheet. The process appears to mimic the mechanics of a sewing machine. A loop is pushed through the hole to the underside. Another thread is passed through the loop.
Looking up &quot;hand stitching awl&quot; presents a method likely to be used in the photo collection. This method uses a single thread, while a sewing machine uses a second thread in a bobbin located under the machine arm.
For this project, the loop is pushed to the underside of the sheet. The awl is removed and placed in the next hole. The new loop is then passed into the previous loop and tensioned.
The new loop becomes the previous loop for the next hole.

From the above image, it appears that the underside thread is pulled mostly to the top. The underside thread is not visible on the underside, but it has to be there and may be the angle of the photograph.
A YouTube video shows one method of connecting the loops, although there may be other methods possible.