Oxide has been taken help from both/all vendors. While AotS's Nitrous engine got its start as a showcase for Mantle - massive amount of draw calls as well as async shaders being the main selling point - it did get worked over for both DX12 and later, Vulkan. It is a fairly objective take on engine development with new lower level APIs in mind. Nvidia cards have a different take on Async Shaders, whether that is better or worse, real or fake, is somewhat irrelevant as there is a way to achieve pretty much the same result. Oxide implemented that at some point. It is worth noting that while the engine is a good showcase at least initially it did not use some of the usual optimizations for example to reduce reliance on excessive draw calls.
AMD/Nvidia have gone back and forth over time when it comes to AotS performance with Nvidia cards barely edging out the comparative AMD cards right now. And by that, I mean DX12 (and Vulkan). AMD's DX11 performance in AotS has been outright atrocious all the time allowing them to claim huge performance increase as DX12 benefit. At the same time, Nvidia cards run DX11 AotS with respectable enough results.
x86overclock, Forza 7 had problems on Nvidia cards that were resolved rather quickly with a driver update. Wolfenstein 2 does have a nice boost for Vega (not all AMD) architecture. The main cause is that iteration of idTech6 using Rapid Packed Math (2xFP16 instead of FP32) for some shaders, leading to some performance benefit. The implementation of some AA modes also tend to favor AMD cards.
DX12 games are not implementing CUDA nor have they ever.