It's not exactly clear in the video, but the structures remain liquid at all times - unlike solder which solidifies on cooling.
A thin layer of semi-rigid oxide holds the liquid in place - like a conductive water balloon.
Very cool stuff, although it seems too delicate to me for any immediate real world uses.
Perhaps a layer of Parylene or some other type of vapor-deposited polymer could make the structures more durable, while retaining its flexibility?