You're probably not setting the DLL override for DXGI.
Yes, you are correct. Using WINEDLLOVERRIDE=dxgi=n helps. However, dxvk_setup.sh tries to do this via adding registry keys. I guess that doesn't quite work then?
I just tried this in a fresh prefix and it's working perfectly fine. Not really sure what you're having issues with.

I think I figured out what's going on. After registry is modified in the script, it takes a few seconds for those changes to be saved into the .reg files into the prefix. And my script was packaging the prefix contents before that save operation happened.
I must be doing something wrong installing dxvk into my local Wine installation. I built a recent version of Wine from WineHQ git repo and built the recent version of DXVK. When launching a 3D application in this set up, I see that d3d11.dll loaded by wine is actually the replacement library from dxvk, however dxgi.dll is still from wine (the built-in dxgi.dll.so). What am I doing wrong?