Why do they have this additional block of plastic around them? Some
kind of shielding?
The plastic is to make them flat so they can be placed by SMT assembly machines. Electrolytic capacitors are round and SMT machines need something flat to work with.
Is there some specific reason they didn't just use the normal "can"
type of electrolytics?
They are a normal 'can' but the pads are SMT pads, it is an alternate way of packaging them. The other way that is typically seed to package electrolytics for SMT purposes looks like this:
The two SMT pads are below and there is a flat top which makes it easier for vacuum chucks to move it.
What type of capacitors are these? Are they still electrolytic?
Most likely electrolytic.