I would call it a minimum.
The thing about ranges for SAMs and AAMs, like you said, is that their effective range changes with altitude, type of target, headings, etc.
All militaries and especially contractors, would naturally use the stated slant range for their SAM against optimal targets as the maximum for their system, unless specified otherwise. So the word "minimum" is in relation to the standard metric for measuring max effective range, and if the real range of HQ-9 is say, 150km+X, then the effective range against various types of targets should be (150km+X)/(A constant for a particular type of target). That is to say, the max range should scale (unless someone more knowledge can enlighten. I am sure it is mor complicated than this)
Measuring max range will only get more complicated in future with proliferation of CeC and off board targeting.