Google Drive API: Is it necessary to be logged in to perform create, delete, etc?

Sorry, but I think your misunderstanding is incorrect. Being authenticated as a user is the only way of editing a file/folder, even if the file is publically editable. The change has to be attested to someone and for that the API needs to know who you are.

This is different to the UI where you can edit a public-facing document when not logged in.