With the distance constraint enabled, no matter what number of points I give the Mesh Circle, or what settings I use for the triangulation, the edges all try to scale to the same uniform size. In the demonstration video the inner edges are clearly not being scaled. Also with a square (4 vertices) it pulls itself into a rhombus on frame 1.
Have gone through the example scene files at least 6 times, double checking every single setting. Opening the example file, the simulation runs as show in the video.