The idea that Neanderthals were less predatory towards nature compared to Homo sapiens, and that this contributed to their extinction, is an interesting hypothesis, but it's not widely supported by current scientific understanding.
Neanderthals were skilled hunters and likely had a similar impact on their environment as Homo sapiens did. Both species relied on hunting large animals for food and used tools made from natural resources. However, Neanderthals and Homo sapiens lived in different environments and had different cultural and technological adaptations.
The extinction of Neanderthals was likely due to a combination of factors, including competition with Homo sapiens for resources, interbreeding, and possibly environmental changes. There's ongoing debate among scientists about the exact reasons for their extinction, and it's likely that multiple factors played a role.
It's important to avoid oversimplifying complex historical processes and attributing them to single causes. Both Neanderthals and Homo sapiens were complex species with diverse behaviors and adaptations, and their interactions with the environment were likely influenced by a variety of factors.