The game crashes with d3d11.dll error. Don't know if I'm doing something wrong. I install ReShade as I usually do, it works for every other game but Bioshock remastered. Assuming there are couple presets that were made using ReShade 3.0+ on "thelazy" site, it should work eh?
I was looking through dxgi.log and found these lines:
Registering hooks for 'C:\Windows\system32\dxgi.dll' ...
> Delayed until first call to an exported function.

Don't know if that's related to the problem or not.

Install it as dxgi.dll.

Edit: This is not a function of your log report. I have it working in my install as dxgi.dll. In fact, I use this as the default hook for all D3D10/11 games.

Well, If I have dxgi.log... I installed it as dxgi.dll which is obvious as this game is dx11 by default.

Odd. I just played through the entirety of Bioshock 2 Remastered along with the DLC and I encountered no problems whatsoever. I'm sure they use the exact same engine.

I guess I figured out where the problem lies. Kinda...
I'm on Win7 and have KB2670838 update installed. I uninstalled it, d3d11 error was gone. Instead I had BioshockHD.exe crash error An article on pcgamingwiki says that I need that update for the game to not crash. I installed KB2670838 update again — same d3d11.dll error with ReShade. The game itself works fine, it's just that I can't use ReShade, which is unfortunate.
Vicious circle.

Alright so I got it working.
For some reason the dxgi.ini wasn't generating all the necessary lines (only 2) it usually does to inject correctly (or w/e technical explanation would be correct). What I did was just copy-pasted a whole dxgi.ini from another preset (Dark Souls 2) to the one within the Bioshock Remastered folder, and set the correct path to shaders and textures. Works fine now.
Weird.