Well, we had quite a few different textures where people had attempted to cover cracks, but I don't think we had any quite a "pointy" as yours! :-) calliope has a good point about trying to knock off the points first. I think it depends on how much time and work you want to put into the walls. We decided to skim coat our messily textured walls with joint compound and sand to a very smooth surface, then just used a medium roller to paint. DH developed quite a skill at this. It takes patience, gradual coats and in some places, like where you repair cracks, feathering out the coats wider and wider until they blend with the rest of the wall. We love how it looks now. I think we did five rooms and it took us most of one summer with both of us working full time. I did the sanding. Invest in dust masks and detergent! Cheers and good luck with your walls!

What you have is two coat plaster. One of the first uses for gyspum panels was as a base for plaster, eliminating one layer (wood and metal lathe need 3 coats). Use Easysand or Durabond. Durabond is VERY hard to sand, so only use it if you can do smooth work. Some bonding compound (really just thin polyvinyl glue) would be a good idea. Mist the surface with a sprayer till just damp, apply bonding agent, wait about 5-10 minutes so the agent is tacky but not actually set, then apply the first layer of setting compound. If you know how to use a plasterer's trowel it will go faster than drywall knives. If you cannot find any bonding compound you can cut white Elmers glue with water to about the consistency of heavy cream. Eucoweld is one bonding agent.

They have compounds which dry in 5, 20,45 minutes, depending on how fast you can work with the taping knife use the right drying-time compound you feel comfortable to work with. Usually, we would use 5 min compound if you have a deep void and use 45 min compound for the last coat if you plan to do the work the same day. If you can wait overnight you can do the last skim coat with a regular compound. They come in small packages (3LB) it should be enough for the base coat for that area.

Hereis a good read for you to get the comparison between the 2 materials.