it looks like an older product called rockote. its basically a polymer modified brick mortar thats used as a non EIFS stucco finish. i think they still sell it in australia, but you can ask at your local old school lumberyard. the old guys there will know what it was and suggest a replacement. if you can't find one, you can use dyna ceraflex 610, but not the 620
That is a rough texture achieved by putting sand or sand-like particles in the paint. From the looks of the first photo, those are very coarse particles.
When you buy exterior paint, grit is an option. Sometimes it is a really good idea, for example, if you are painting porch steps where you need friction to avoid slipping and falling.
I would scrape and sand away the damaged paint. Anything loose has to go. Next, buy a good quality exterior paint designed to bond to concrete. The store can tint and add grit for texture. Apply the paint following the manufacturer's instructions (it may require special primer or the surface may need to be prepped somehow).
I also recommend inspecting the underlying concrete for damage after removing the paint. If there are cracks, they may need to be repaired before painting to avoid further trouble with that section.
As has been mentioned course washed sand has been mixed into an exterior house paint, but it failed to adhere to the cement surface. This may be due to poor prep work or non-compatible ingredients in the paint.
It's best to scrape/wire brush the loose paint followed with a scrubbing of water to remove dust. Note if the water is being absorbed by the cement wall. If so the surface is open and porous so it will accept paint readily.
Use a paint specifically for masonry. Several are available; the most common is the Dry-Loc brand. I've used this with good results. It will dry with a rough texture and can be tinted to many colors if needed.
Another alternate technique, but more labor intensive is to mix a very loose stucco patch to the consistency of syrup. Add enough fill sand to match the existing rough texture and with an asphalt or course brush "throw" it onto the wall.