AFAIK (I have a similar soft shadows system based on SDFs) the reason the noise issues occur in small gaps is that the distance values become small there so the steps become small and you start ending up in artifact land. The workaround for this is to enforce a minimum step size of perhaps 0.5 - 2.0 pixels (depending on the quality of your SDF) so you don't get trapped like that - the author probably knows but it's not done by their sample code.

Small step sizes are doubly bad because low-spec shader models like WebGL and D3D9 have a limitation on the number of loop iterations, so no matter how powerful your GPU is the step loop will terminate somewhat early and produce results that don't resemble the ground truth.