Over time, UV light can break the chemical bonds of a polymer, causing degradation. The major problem, however, is that the dashboard just plain dries out. Polymer additives called plasticizers dissipate over time. Plasticizers These are materials added to a polymer to lower the glass transition temperature. The plastic curtain has added plasticizer to make it soft and flexible.
Plasticizers are usually small organic molecules.
Over the course of many years in the summer sun, the plasticizer dissipates. You don't see the bottom layer which is a glass-fiber reinforced thermoplastic. On top of that is a layer of polyurethane foam. ABS is an acronym for a block copolymer made of acrylonitrile, butadiene, and styrene. PVC blended with ABS effectively does the same thing as PVC with added plasticizer, but in this case, the ABS doesn't evaporate so the dashboard lasts a lot longer.