Yeah I noticed this problem just now. Not sure why it's like that unless I actually leave my browser on for 1 week for it to work properly.
Edit: Log out, log back in and click the first stamp. This seems to fix it.
On GOG.com you can score yourself a free copy of the game by scrolling down a little to find the promotion. Click the first ticket and there will be a timer until the next time you can collect one. Repeat that for one week.