The stags in the pictures for this hunt are farm bred animals. That stag pictured is as used to people as your pet cat.
Wild red deer do not grow heads like that, and these stags do not live long. Their skulls can crack open from the weight of the antler they are not designed by nature to carry.

Deer on the private properties that are selling hunting packages are virtually all farm bred and managed animals. They will call it 'free range' which it can be sometimes technically, but the animal itseff was living on a farm until a month beforehand. If an operator is offering gold/wilver/branze animals, then they are definately farm animals and even can be handfed. One famous example was shown on the internet after the shooting, in a safari pose ($20K worth) - later a picture surfaced with the same stag being handfed apples earlier.

The stock trucks round here are very busy in March each year trucking all the farm stags sold at auction out to the "game estates" where they are released ( into a paddock ) into the hunting grounds.
The 'guides' have photos of these animals taped to the fridge door so they can remember which one is which and where they are found on the property. These are hunting theme parks. There is no way any kind of world record could stand in any hunting organisation based on those stags.

There is no regulation of guides or outfitters in NZ, and they are not the same kind of businesses. A 'guide' may not the same kind of thing you will be familiar with in the United States, nor is he a ghillie like in Scotland.

Sharpsnitro, despite game estate salesmen who tell foreign hunters that nz deer is all shot out and the helicopters have killed everything, it is still possible to shoot wild red stags in the NZ mountains for free, in the national parks, using the hut system. Best time of year for an overseas hunter is April, during the roar.
Tahr are easy.
A fair level of fitness is required for hunting in NZ - it's all backpack hunting to a degree, although it can be as hard or as easy as you want to make it.