Here’s the thing: mankind has been impacting wild ecosystems and changing them for thousands of years.
Beginning in Africa as far back possibly as a million years ago, we began to change and assert our presence on the landscape through the intentional use of fire and stone tools. We used fire to maintain the savannas and grasslands that we and our ancestors favoured, and thereby the food that we found - be it antelopes or the tubers and other edible plants that grow in savannas.
We carried the tradition across into other regions around the world as we left Africa and spread across Asia into the Americas and Australia, bringing vegetative changes to the ecosystems and leaving megafaunal extinctions in our wake.
Those same traditions continued in the New World, with Native Americans having techniques to promote the kind of landscape that deer and other prey preferred. The Aboriginals in Australia also have their ‘firestick farming’, where again the use of fire is used to encourage the sort of habitat that prey like kangaroos and reptiles favoured.
In fact, there is a circulating theory, supported with some evidence, that the Amazon rainforest is a result of human cultivation:
Keeping the above in mind, is it useful to ask if a particular ecosystem is ‘wild’ vs ‘cultivated’? Seeing as humans have modified ecosystems for their own benefit for thousands of years, we could technically call such ecosystems “cultivated” even though modern sensibilities treat these as wild.
Aside from particular areas deep in the frozen wastes of the polar regions, there is hardly anywhere a landscape that hasn’t been shaped, modified, or otherwise untouched by humankind.
In fact, many endangered species are clinging on only because we as a species have made the conscious effort to set aside habitat for them, boost their numbers through cultivation/captive breeding, and intentionally “restore” lost habitat for them, such as in the example mentioned in the OP. When we reintroduce them to the ‘wild’, that in itself is another human change to the ecosystem, however benign (and even beneficial).
Many ecosystems and landscapes in national parks, to this day, require some level of human management - for example, the occasional controlled burns done in South African nature reserves to rejuvenate the fynbos, grassland, and savanna ecosystems where such species are clearly fire-dependent as part of their lifecycle. Yet no one would dream of calling any of these animal and plant species as domesticated in any shape or form.
‘Wild’ and ‘cultivated’ blur together when one takes the long view through a historical and prehistorical lens.