First thing I found was this key:
So I cross-referenced the UUID and found this key:
So I searched for ContextMenuHandlers MSDN on google and found this page:
That page explains how the other Windows editors are achieving their magic. Specifically, under the first topic:
Because shortcut menus are often used for file management, the Shell provides a set of default commands, such as Cut and Copy, that appear on the shortcut menu for any file system object such as a file or a folder.
So it would seem that what you want, if you want to enable similar behavior as other popular windows-based text editors of the day, is to create a "default" command.
I'll also make a note that Windows context menus support Shift+RightClick for an "extended" context menu, which (for example) enables the Windows built-in CMD Prompt Here/Powershell Here actions. I personally like to utilize that to organize less-often used items. For example, I'd happily delegate 7-zip to Shift+RightClick, if it was an option in 7-zip. I personally want my "Open with Text Editor..." option to be a regular Context Menu action but figured I'd mention it since it might be a config option worth considering for others.