2009 (I can't link directly to the Details tab or the forum will throw a fit). So the page was definitely revisited after, since they couldn't have recommended AMD drivers from 2013 from the start.
To be fair, Discover games - New section has most of the same information.
I also find the Show More link below that more useful. You can filter by New Arrivals, sort by Release Date (from newest), but without a 7-day cutoff.

Discover games — New section shows only 10 last arrivals and sometimes GOG adds more than that on the same day (especially when they release games with zillion DLCs and editions).
And sort by release date is just broken (and has always been, I think). It lists games in seemingly random order that has nothing to do with their release on GOG. Previously there was option to sort by date added that worked like expected, but GOG got rid of it with redesign of search page.

Yeah, I just noticed both these things with the latest sale. What a shame. I'll post about the "newest" sorting option in the new catalog announcement thread. I don't know if it's still monitored for feedback, but it beats waiting ~5 weeks for support to respond.

Do you have any idea after what time this "new" flag is removed from a game (which makes the game get listed under "New arrivals")?

No, because as mentioned above, the Release date (from newest) sorting option is broken. So I don't see any way to find out, besides opening all the listed games in a new tab, and see what the oldest release date is.

It's not related to the release date of the game. It's related to the arrival on GOG. At the moment there are several games marked as new (like the Giant series games), which have been released more than 20 years ago.