Glad to hear you are making progress on your project.
Please take a few moments to learn how to use CodePen, Plunkr, jsFiddle or any other free online html editor.
It doesn't require much more than copying and pasting your html, css and js into the appropriate panel and saving.
The demo below already loads TweenMax and Draggable. Just "edit on CodePen", fork, add your code and save:
Trust us, it is soooo much easier than saving html files uploading them and making us download, look, edit, upload etc.
From your demo it looks like the divs spin freely and fine when you drag. ThrowProps is responsible for the movement that occurs after you release – that super smooth flick and spin action.
You are probably still getting re-directed to the GreenSock site because you are still loading the ThrowProps script. Remove this code
In order to detect which card should have it's z-index changed you could maybe use an onDrag callback to get the rotation of the Draggable. Based on the rotation of the Draggable you should be able to determine which card is facing up.
So if you had 4 cards spaced at 90 degree intervals (0, 90, 180, 270) and you rotated 180 degress you would change the index of the third card. You would probably want to build in some sort of padding so that you can detect whether or not a card is within a 5-10 degree range of each interval as the rotation will probably never exactly equal 0, 90, 180, or 270 (unless you are using snapping). And then once you set the z-index to 1 I suspect you will need to turn it off when they spin again. Draggable can generate the values you need and has a wide array of callbacks but there is still a decent amount of custom code involved to get it to work. There is a ton that goes into building a site like you referenced. It was ground-breaking when it came out years ago and still is.
There may be an expert around here who can whip something up but it isn't the type of use that is built into Draggable. We really do our best around here to help where we can with questions related directly to features provided in the GSAP API, but unfortunately we just don't have the resources (time) to be able to try to re-create these types of cutting-edge effects. A project like this would easily take me hours to set up and try to build the right way.