Traditional Arabian falconry - as practiced in Arabia, with falcons flown from the backs of camels, that were released back to the wild at the end of the season, was once an activity that had limited impact on predator and prey. But what it has morphed into bears very little resemblance to what is so often invoked in connection with it - its tradition. Luxury SUVs, international travel via private jets to distant regions such as Turkmenistan, and stables full of hybrid gyrfalcons, kept in air-conditioned quarters over the summer season, are a far cry from how the pastime was practised even by the fathers of the current rulers of the KSA and the Gulf States - much less releasing bagged quarry (mentioned in the link in the original post) which would be scorned by any true practitioner of the art.
The pursuit of wild houbara and other quarry with trained falcons does indeed have deep roots in Arabian culture and heritage, and done in the traditional manner it was sustainable. With better management of the environment, quarry species, and the falcons, it could become much more so. But whether its modern day practitioners have the self-awareness to realize that what their pastime has become has far departed the traditions of the past - let alone the desire to reform some of its more egregious practices - is doubtful to say the least.