To resolve this OBS Studio error, simply update your graphics card drivers. I suggest downloading the Nvidia GeForce Experience program from their official website. Once installed you can log in using your Nvidia account and update drivers automatically. Make sure to perform a clean installation and then after restarting your computer click "Optimize all games & apps."

This will fix following error messages:

Failed to open NVENC codec: Function not implemented
Please check your video drivers are up to date.

Your current video card driver does not support this NVENC version, please update your drivers.

Starting the output failed. Please check the log for details.
Note if you are using the NVENC or AMD encoders, make sure your video drivers are up to date.