I wondered and wondered what I could use to make it spring back shut and finally, after reviewing several YouTube videos, realized it was pieces of metal tape measure that were cut and inserted in the pockets at the top. I went to our local dollar store and could only find 1" wide tape measures - which were too wide for what I wanted. Finally at WalMart, I found a 3/4" tape measure that was the right price - under $5. Don't use good scissors to cut the metal tape measure! Round the edges and cover with tape so you won't have sharp metal edges wearing away at your fabric.
The videos I reviewed were this one, and this one. But the best tutorial was this one, which had instructions for a lined snap bag with seams that aren't exposed. It was a little fiddlier, but I really liked the result.
I also used medium weight fusible interfacing which I cut slightly smaller than the main fabric pieces.
I added the little black and white tabs (2" lengths of ribbon folded in half) in the centre of each side to have something to grab to open the bag. It was just a 2" length of ribbon folded over and stitched into the casement seam.
If you don't have ribbon to use for the opener tabs, you could cut two 2" squares of the lining fabric and make tabs by folding each in half, then unfolding and folding each raw edge into the centre fold and stitching the sides together - like bias tape would be (except this wouldn't be on the bias). Or you could make prairie points or even use bias tape in a coordinating colour.
As for the tape measure, make sure you keep it locked or you will lose the cut end inside. If that happens, just take the case apart, removing the screws, and retrieve the end. Beware, the mechanism is spring-loaded and could explode in your hands.