No.

Short answer...no.

Because the games are DRM-free, once you've downloaded it...
But because many games are old, and updating to modern systems can sometimes be problematic or quirky, tech support will help to fix the problem, but on occasion, cannot. Hence, the refund option.

As far as I know - no. If it's not about technical issues and you already downloaded the game, you can't have refund (if I didn't miss something in the meanwhile).

edit: Sorry, when I've started to write this post, I didn't see yet two above.

OK thanks for clarifying and makes sense.

No, unless the game is an In Development one.

GOG offers 3 Money Back options.
Option 1 is the "Oh, didn't mean to buy this game" one, which allows one to return a game he hasn't downloaded within 30 days from buying it.
Option 2 is the "This doesn't work" one, which applies if a game has severe technical problems, you've notified support within 30 days of buying the game, but support was unable to help you.
Option 3 is the "In Development" one, which allows you to get a refund for an In Development game you bought in the last 14 days, no questions asked.

You can also cancel preorders at any point up to the game's release. For more info, see section 6.7 in the user agreement.