What kind of wall is this (plaster?), and how do I repair it?

This is an interior wall in the house I've rented for the last three years. As you can see, a housemate's hanging hooks didn't last very well and ripped out of the wall, taking chunks along with them.

There are also a half dozen holes made by drywall anchors that I'm not sure were installed correctly. The person seemed to have a beast of a time putting them in.

I know how to spackle smooth drywall, but this stuff is textured and off-white. How do I patch it up before move-out?