Finally, I’ve solved this; Geforce Experience (GFE) is the main problem. I tried older versions and v2.5.15.46 worked well and black bars are gone (The latest GFE Beta version is not running with Moonlight OSMC). Like you said, screen resolutions should be equal on PC and RPi for best experience.
I use Xbox 360 Wireless Gamepad but some buttons (i.e. right trigger) of controller suddenly stopped responding. If you connect a gamepad to your PC, GFE can cause some problems because the emulated Shield controller appears to games as Controller 1 (If you run Xbox360 Gamepad utility, you’ll see 2 controllers).
Here is the solution (32&64bit):
- Navigate to C:\Program Files\NVIDIA Corporation\NvStreamSrv
- Rename rxinput.dll to rxinput.dll.old
- Do it again on X86 folder: Navigate to C:\Program Files (x86)\NVIDIA Corporation\NvStreamSrv
- Rename rxinput.dll to rxinput.dll.old
Plug your Xbox 360 controller wireless receiver into your PC. It’ll work flawless now and you don’t need to plug it on RPi.
Also, you should stop GFE auto-update:
- Navigate to C:\ProgramData\NVIDIA Corporation\GeForce Experience\Update
- Delete setup.exe
That’s all! So I can play my games on my big TV 
Thanks @exxe Keep up the good work!