I have the exact same problem. (with the 403 as well as the downloader)
I posted a ticket to GoG support and this was their answer:
Hello
We apologize for the inconvenience. We are currently investigating this behaviour on our end, however finding the cause will take time. This is not a global issue, and we are trying to isolate why this is happening to a certain group of users.
We will let you know as soon as the problem is fixed, or when we know more about the underlying issue.
Regards,
JuriJ
GOG.com Support