It’s not soft touch paint, since soft touch paint is just a coating on a hard (non flexible surface).
It is either an injection molded TPE (Thermoplastic Elastomer) or TPU (Thermoplastic PolyUrethane).
This is the same type of molded material you’ll find on your tooth brush, or smart phone case. It’s better for overmolding/dual shot parts since it bonds better to substrate materials, and can be shot in a range of very hard to soft durometers.