The Mongol great hunts, or nerge, did indeed constitute massive hunts throughout the steppe. Their purpose^1 was at least twofold. On the one hand, it was to gather meat to see the Mongols through their harsh steppe winter. On the other hand it served a military purpose. The hunt lasted for three months^2 and involved the entire army in full battle dress, initially assembled along a line 80 miles long.

Once it began, it drove before it all living things. As time passed the wings of the hunt slowly contracted to form first a semicircle and then a circle. The circle then closed in on all the game, and if an animal slipped past the ring, the responsible soldier and his officer were punished.

Eventually the Khan would let the slaughter commence and everything was killed until the tribal elders deemed enough was enough. Morgan uses a quote from Gibbon on the subject, which I'll reproduce:

The leaders study, in this practical school, the most important lesson of the military art: the prompt and accurate judgement of ground, of distance and of time. To employ against a human enemy the same patience and valor, the same skill and discipline, is the only alteration required in real war; and the amusements of the chase served as a prelude to the conquest of an empire.

So the hunt was vital for building discipline, teaching leadership to the officers and cohesion among the ranks. Juwayni the Persian chronicler remarks that war was " analogous in every detail" to these hunts. Neither of those books includes the effects of the hunt on ecology but I can imagine they would be vast in the short term, but an allowable slaughter over the long term for these hunts to continue.

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^1 The Mongols, David Morgan

^2 Genghis Khan's Greatest General, Subotai the Valiant, Richard. A. Gabriel