When a script uses oAuth (googleOAuth_(name,scope) in you case) it needs to be authorized from the script editor, independently from the other authorization that the user grands with the "normal" usual procedure. This has been the object of an enhancement request for quite a long time and has no valid workaround as far as I know.
So, depending on how your script is deployed (in a SS or a Doc or as webApp) you might find a solution or not... if, as suggested in the first comment on your post, you run this from a webapp you can deploy it to run as yourself and allow anonymous access and it will work easily, but in every other case your other users will have to open the script editor and run a function that triggers the oAuth authorization process.