I logged in to my GoG account and I see the few newly purchased games are labelled as I tried out after the purchase immediatly.
But I didn't tried out quickly, although there should be the "new" prefix.
I don't know if this occours with others as common issue?

Perhaps someone else has access to your account and tried them out for you?

Did you klick on the game to just look at the links? That would remove the "new" label, too!

I've noticed that a all new labels disappeared this week as well (had a few – I haven't downloaded the free games from the last sale so far).

As rbstego indicated, expanding a game "tile" will clear any "new" or "updated" status -- the latter immediately (IIRC), the former only updating when the page reloads (at least in a normal browser -- no idea if it works this way in Galaxy). This occurs whether or not you clicked on any download links.
So if you want to open the tile, but don't want to download the contents right away, maybe add a custom tag. The one I use for this purpose is called "not yet downloaded".