The author finds "some good data on Wikipedia" (respect!) showing that the "lithography size" will be reduced from 32nm in 2010 to 11nm in 2022. He calculates this to be a "volumetric improvement" of 50%. There I was thinking that it was an 846% improvement, but I hadn't taken the third dimension into account.
Nevertheless, I think the author has a point, but he is missing part of the picture: NAND flash SSDs may not replace HDDs any time soon, but other types of non-volatile memory may well do so.
HDD densities will probably increase, but the slow access and transfer times and the static unrecoverable error rate will probably relegate them to use for back-ups or as cheap mass-storage devices for non-critical data. SSDs, however, are not restricted by the limits of NAND flash. Non-volatile memory technologies such spin transfer torque RAM and phase-change RAM have a good chance of replacing NAND flash memory in SSDs. These technologies are available today. Memristors are probably the most exciting development, as they promise a breakthrough in memory density. HP have a memristor-based design that could make petabyte SSDs possible, but we'll probably have to wait a few more years to see if that pans out. There are also major advances being made in fabrication technology, with cheap "printable" electronics already in consumer devices.
Real random-access memory that is cheap, reliable and fast is probably only a few years away from the mass market. There is so much money to be made by such an advance that R&D spending will not be lacking. So, the author is wrong; SSDs will dominate in the near future, just not NAND flash SSDs.
P.S. I don't have any SSDs because they are too small and expensive compared to my 1TB HDDs!