This is an old thread but as I hit the same issue and found a workaround thought I'd share it.
It's a similar issue some people have hit (including myself) with Sherlock Holmes: The Devil's Daughter. Someone posted a fix for this and when I realised it was the same game engine (Unreal) gave it a go and it works so you can use the mouse.
1) Go to C:\Program Files (x86)\GOG Galaxy\Games\D4 - Dark Dreams Don't Die - Season 1\Engine\Config
2) Copy and paste BaseInput.ini to make a backup
3) Open BaseInput.ini
4) Remove the section:
; --- XBox Bindings
;Bindings=(Name="XboxTypeS_X",Command="Use")
;Bindings=(Name="XboxTypeS_A",Command="Jump")
;Bindings=(Name="XboxTypeS_B",Command="ChangePosture")
;Bindings=(Name="XboxTypeS_Y",Command="NextWeapon")
;Bindings=(Name="XboxTypeS_Back",Command="")
;Bindings=(Name="XboxTypeS_Start",Command="|onrelease showmenu")
;Bindings=(Name="XboxTypeS_LeftShoulder",Command="obj list")
;Bindings=(Name="XboxTypeS_RightShoulder",Command="mem")
;Bindings=(Name="XboxTypeS_DPad_Up",Command="MoveForward")
;Bindings=(Name="XboxTypeS_DPad_Down",Command="MoveBackward")
;Bindings=(Name="XboxTypeS_DPad_Left",Command="TurnLeft")
;Bindings=(Name="XboxTypeS_DPad_Right",Command="TurnRight")
;Bindings=(Name="XboxTypeS_RightTrigger",Command="Fire")
;Bindings=(Name="XboxTypeS_LeftTrigger",Command="ToggleTargetingMode")
Bindings=(Name="XboxTypeS_LeftX",Command="Axis aStrafe Speed=1.0 DeadZone=0.3")
Bindings=(Name="XboxTypeS_LeftY",Command="Axis aBaseY Speed=1.0 DeadZone=0.3")
Bindings=(Name="XboxTypeS_RightX",Command="Axis aTurn Speed=1.0 DeadZone=0.2")
Bindings=(Name="XboxTypeS_RightY",Command="Axis aLookup Speed=0.8 DeadZone=0.2")
// trigger deadzones roughly correspond to XINPUT_GAMEPAD_TRIGGER_THRESHOLD / 255
Bindings=(Name="XboxTypeS_LeftTriggerAxis",Command="Axis aLeftAnalogTrigger Speed=1.0 DeadZone=0.11")
Bindings=(Name="XboxTypeS_RightTriggerAxis",Command="Axis aRightAnalogTrigger Speed=1.0 DeadZone=0.11")
5) Save the file
6) Play the game!
Haven't worked out a way to use the controller instead but the mouse is fine for me on this game. Usual I'm not responsible for any damage you do to your PC etc. applies.
