This is a really inventive use of the global distance field! Awesome stuff.
Well you can only sample it on the GPU in a material graph, so it needs to be visual-only effects. 's soft body approximation is just a visual effect, the actual collision between the balls is using the standard physics.
One thing I am curious about , are the spheres themselves in the distance field? Static meshes are in the distance field by default if they cast shadows and have ‘Affect Distance Field Lighting’ enabled. If the spheres are in the distance field, usually you get a distance of 0 when you do a DistanceToNearestSurface with your own position. But if the spheres aren’t in the distance field, they would not squish each other.