…and is only sewn to the tops of the card slots and through the centre on the fold
With the multiple layers, and the flexibility needed in a purse (or wallet) you really don't need a thick vinyl. I'd say 0.8 to 1mm is all you'd need. I've toyed with making eco-leather wallets, and 1mm is the maximum I was happy with.
Although it looks like there is stitching in only at the top of the slots and down the middle, there is almost certainly more stitching (or glueing) inside the card slots. If there weren't, the pockets would be too deep and cards would disappear within!
Have a look at some of the "long wallet" making videos on YouTube.