There is no auto-completion because the script says "Miscellaneous Files" instead of the of the name of the Project. Take a look at the image below that came from the video in your question:
The "Miscellaneous Files" message can happen for many reasons:
It can happen when you open your Unity C# file from another folder instead of opening it from Unity Editor.
This can also happen because Unity crashed while Visual Studio is still open therefore corrupting some files.
It can happen because Unity was closed then re-opened but is no longer connected to Visual Studio. When Visual Studio is opened you get "Miscellaneous Files" and no auto-completion.
This can happen when Visual Studio Tools for unity is not installed.
When you create a script from Unity then quickly open it before Unity finish processing it or before the round icon animation stuff finish animating.
Most of the times, restarting Unity and Visual Studio should fix this.
I can't tell which one is causing the problem but I will cover the most likely solution to fix this.