As every corporation that sell goods and services GOG has different departments. Depending on what problem you have encountered and reported via ticket system ZenDesk forwards your ticket to an appropriate department.

BUT :) Sometimes the support guy can open your ticket, while he has other things currently to do, and simply forget about your ticket. It happens all the time when the platform has too many tickets while having too little assets to solve them up. And believe me the number of tickets customers create strictly depend on what quality of your services are.

Are you positive the ticket is still open after all that time? Did you try adding one reply to the ticket, to "bump" it in the list?
That's normal. Check the status of the ticket on the site, using the link you got in the confirmation e-mail for opening the ticket. If don't have the link but you remember the ticket number, just replace the number at the end of this link:
https://support.gog.com/hc/en-us/requests/1501605
Note the site may prompt you to log in, but not show the ticket automatically. Load the link a second time.

Edit: typo.

Deleted.

Ah thanks. I was looking at the plaintext version of the confirmation email, which doesn't have a link in. It's been reopened.

Yes.