Great question! This result is in the same area as the work on the amplituhedron. It's not immediately obvious to me that they are directly related, and I didn't see a reference to any amplituhedron papers in the citations of this paper. Dixon et al. have essentially discovered a new symmetry which the scattering amplitudes (of N=4 Super Yang-Mills) must obey, and new symmetries generally lead to deeper understanding of the theory. This symmetry should then also be somehow encoded in the amplituhedron description of the theory; I imagine people would look into this in the future.