The author of that article is applying Voyager-era warp speed concepts to TOS which I think is a huge mistake. The original Enterprise zipped to the galactic rim twice (in "Where No Man Has Gone Before" and "By Any Other Name"), back to Earth, and the centre of the galaxy twice ("Magicks of Megas Tu" and Star Trek V: The Final Frontier
). In "That Which Survives" the old Enterprise explicitly covers 1,000 light-years at warp 8.4 in 12 hours (for comparison, a month at that speed and they would have made Voyager's 75,000 light year journey!) The new movies are 100% in line with those. It's Voyager and the (non-canon) technical manuals which depicted warp speed as far slower than it used to be.