(Author here.) Did you see the faces example on the GitHub page? It was a domain-specific network trained adversarially for that purpose, but I have yet to see any super-resolution of that quality with or without machine learning.

Most other approaches don't even try to inject high-frequency detail into the high-resolution images because the PSNR/SSIM benchmarks drop. Until those metrics/benchmarks are dropped, there'll be little more progress in super-resolution.