I have read the following threads:
I see the same behaviour. Interestingly, I cannot even open the Script Editor as an anonymous user to confirm the script is there, although that menu option is not grayed out.
It all works fine once I log into an unrelated account.
This may be a bug, or it could be an undocumented restriction, or it could be a temporary issue that will get resolved.
I think you've set up everything correctly.
Scripts cannot be accessed or run at all by anonymous users, unless they are deployed as a Web App, and even then only the front end is accessible by an anonymous user.
You'll see in your bound script that users who are not logged in cannot even access the script editor by clicking tools -> Script Editor (But all logged in users can). Additionally, if you have a standalone script in your Drive, and you right click and share to 'Anyone on the web can edit', anonymous users are still required to login.