To build the 3D model, they looked at the elements inside a supernova (such as iron, silicon and argon) and the light they emit when heated. That gave them a way to figure out how fast the supernova's debris are moving and in what direction. The result is a visualization showing the spherical component making up the outer parts of the remnant and the flat, disk-like component making up the inner part. You can also see high-velocity plumes or jets shooting out of the structure:

Since the team created the model specifically for other astronomers building supernova models, it's unfortunately not that easy to get your hands on it. You'll have to contact Kimberly Arcand, the Visualization Lead for NASA's Chandra X-ray Observatory, to get the open access files for VR caves (immersive VR rooms) and for the Oculus Rift. The team is also working on a Google Cardboard version, so you may want to wait a bit before sending in a request if that's your preferred device.