Yes, the frictional dampers are basically brake pads that clamp tight around the towball. The gas struts that you saw have nothing to do with stability, but they dampen the fore/aft motion that at the same time controls the overrun brake. Without them the trailer brakes would come on and release again all the time, totally uncontrollably.
AlKo have by far the biggest share of the market as far as electronic stabilisers are concerned, but there are a couple of others, like BPW's iDC system and the father of them all, the LEAS system, but they all work on the same principle. They detect lateral acceleration of back of the trailer and if that exceeds a threshold value they mechanically apply the trailer's brakes lightly through an electric actuator, just enough to pull it straight again.
Electric brakes for trailers are very rare in Europe because they require some sort of proportional input signal from the towing vehicle. On the other hand they must also be fail safe and apply the trailer's brakes in the event of inadvertent separation from the towing vehicle while in motion. As there aren't any provisions for transmitting necessary signals in the standard factory-fitted electrical system of the towing vehicle to the trailer, this would have to be retrofitted. However, any such retrofitment would amount to a technical modification that needs to be approved by a vehicle testing authority and documented in the vehicle registration papers. Simply because of the administrative work involved, this makes electrical brakes a rather unattractive option, quite apart from the fact that it limits towing vehicle and trailer to just one specific combination without the ability for any interchange of the trailer with another towing vehicle not so equipped. For that reason, mechanical overrun brakes are the norm for trailers under 3500kg. Over that, trailers do need an independent braking system, but this is usually in the form of an air brake.