Range figure means different things in different missiles. Sometimes range means that system is still absolutely deadly and lethal to the outer edge of its threat envelope. It's absolutely the case for HQ-16C.
Sometimes, system is thoroughly optimized for range, that ironically it can extend reach literally at expense of utility: for example, the longer and slower your rocket somehow glides, the more cooperative target can manage to approach. This gives you a lot of Dmax.
Some of worse offenders in this particular case are CAMM/CAMM-ER - rather light missiles with slender aerodynamics, which go for all possible crimes to get range.
Now to our specimen.
Both ESSM and HQ-16(Shtil, Buk) are originally close-medium range systems. Both are quite large for their original ranges, but Buk is huge(SM-2 class).
ESSM mk.2 was a relatively more recent, thorough and range-optimized upgrade, while HQ-16C was still direct ascent all the way to the outer edge(even from VLS).
When HQ-16F did trajectory optimization(and longer batteries) - magic happened, range doubled.
Note that Russian Buk-m3 (or active Shtil) still flies same 70 give or take, because instead they now include 9A83s in Buk batteries for 150km capability(Soviet Union produced so far too many S-300Vs for Russia anyway).
