I think one big difference between Pakistan and other countries that have managed to conserve wildlife and landscapes without hunting (India, Kenya, Botswana, Uganda) is that there is little to no potential for large-scale international photo-tourism in the markhor's range. The terrain is not conducive to anything but hardcore hikers and mountain adventurers, and there aren't too many charismatic ABC species. Also, the reputation as an unsafe conflict zone isn't entirely unjustified.
No one can deny that hunting has played a huge role in conservation, and is still useful in many cases. I think the hunting lobby overstates the importance of hunting over photo-tourism in much of Africa, where there have been studies showing that photo-tourism can bring more community development and thus conservation in the long run. Pakistan, for the foreseeable future, might be their actual strongest case.
Still, I think it's a strangely good thing that a lot (or, well, a tiny but vocal and influential segment) of Pakistanis are outraged at the hunting of markhor. It shows a measure of local/domestic concern for the species which is the first and most important step to any kind of long-term conservation.