So, I'm just going to jump right in. I'm not going to include evidence, since there's quite a bit (and I'd have to black out sensitive information), and am just going to paraphrase. If, however, you want evidence of a specific part, let me know.

During the Gog Fall Sale, I spent a lot of time browsing the store for some nice games to pick up. I purchased quite a bit, but then I saw the Jackpot! Minecraft: Story Mode was on sale for half off! My sister would love that! I quickly throw it in my cart, type in her email address and send it off. Later that day, she opens the email and creates a new account to redeem the game with.

She loves it, and it's going so well! But then... Close to the end of episode 1, trouble happens. A game breaking bug prevents her from killing a Ghast, keeping her from continuing on to the end of the episode.

For most games, this would be the end of the story. I had my fun, but the game is now buggy, and I don't feel like playing. But this is my sister we're talking about... And this is freakin' Minecraft Story Mode! There's no way we're giving up on this!

So, I write an email to Telltale Games! Hey! There's a game-breaking bug in here! I provide a YouTube video. They run me through some fixes, which I'm forwarding to my sister so that she can do them. Slowly, the fixes become more desperate. By week two, they insist that we completely reset the game! Purge the save files, redownload from Gog, and replay through the whole thing. Well, my sister decides to comply. It still doesn't work, and that's the last we heard from Telltale Games.

My sister, pretty frustrated at this point, decides to email Gog Support and asks to exchange the game for something different. She gets the response back that since it was a gifted item, the 30-day money back doesn't apply.

Hmmm... Let's take a look at the Gog 30-Day Money-Back Guarantee:

Can I get a refund for a gift I've received?
Since you did not pay for the games yourself, we can offer you a replacement game of equal or lesser value, as a form of store credit. If the person who purchased the gift prefers to receive a full refund, this is possible, however, they should contact us about this separately.

Alright. So, something is screwed up there. I guess I'll email Gog myself, then. Maybe there's some weird technicality since it was a gift. Type, type, type... Please refund this game into my sister's account so that she can exchange it for another. Here is a PDF of the email conversation I had with TellTale, and a video of the bug. Insert a few more details... And send.

A few hours later, I get a reply: We are sorry, but we're not allowed to provide a refund to a functional game.

Ummm... Excuse me? The game is *not* functional. You even say in your money-back guarantee that "If...you experience technical problems or game-breaking bugs that prevent you from finishing your game, contact our customer support."

Type this into an email, and....

Gog: "Unfortunately I cannot grand Wallet funds to your sister account."

The last email I've gotten from you guys are asking to troubleshoot. I understand that there's procedure, however, we've already gone through this with Telltale Games, and are feeling very disappointed that I have to play telephone with my sister again. In addition, it's apparent that you have not read my emails in detail, as the computer my sister uses is a Mac, and the troubleshooting directions you've sent are for Windows. At the very minimum, you should have opened up the troubleshooting with my sister when she tried to contact you rather than through me, when I don't have direct access to her computer.

As for the part of TellTales, I believe it. I also had a lot of problems with their "customer support", the only advice I can give you is to never buy a game from TellTales anymore.

For the Gog part just insist again and if necessary contact someone from the staff here on the forum.
Even to me, it happened that they did not understand the situation, but in the end they always solved the problem.
Explain the problem in the mail back saying by pointing out that they sent the wrong informations for windows instead of mac, that you already contacted TellTales and that TellTales don't solve the problem, that you want them to contact your sister and that you want a refund because of a game breaking bug.

I got a refund for a game breaking bug on mac for a similar reason (graphic glitch, invisible characters) on Legend of Kay. Also I got a resolution for a bug in the audio episode 2 of Tales of Monkey Island (from TellTales the only game I got from them).

Also you can get a full refund, not just gog wallet if you used a credit/prepaid card to pay.

Yeah for security and legal reasons they arent going to give your sister the money as you are the one that paid for it, so my advice is to request a refund for you and try again to explain the situation and provide them the evidence i.e show GOG support your emails with telltale about it.

You should be able to get a full money refund.

But sadly its now the weekend so you might not hear back from them until Monday at the earliest.

and if it fails well, I dont know at that point.

Avoid Telltale games in the future, like Lief above me, I have been burned by their games before (on steam and this was BEFORE refunds there), they are lazy and they dont care if you have issues "oh we will get around to fixing it, but you know we are working on our next game that you should buy" so I dont trust them and ignore their releases.

But if it doesn't work send an inquiry to support as long as you are respectful they should help you.

Well you might have run into someone from gog support who was not really able to understand your email. Sadly that happens not sure if some are just not reading the mails correctly or what the problem is, but it happens. Don't give up. Like the others said, write to them again in a new ticket (because hopefully then it will end up with someone else) and if nothing else helps write a chat message to one of the blues here on the forum.

Same way i feel about Nihon Falcom Corporation, Mastiff and their end game credits crash in gurumin,so one can't play new game+ to unlock all of the clothes in gurumin and in the end i just let it go and decided to not buy anymore games from them.And several users had this problem with gurumin,don't know if anyone was capable of getting a new game+save game in the game.
Gog isn't perfect that would guarentee all games working properly.

Hmmm, me as well as a few of my nieces who have played Minecraft Story Mode from GOG, and have all played through episode 1 multiple times without issue. Just to give you my experience.

This is probably why GOG support thinks it's a functional game, because they are probably getting very few if any reports saying otherwise. Is it possible your sister is confused on how to properly proceed in the level? It would not be the first time that has happen to someone while gaming and they then think it's a bug. Maybe providing a link to the youtube video of the bug can help us help you more?

Not saying you are wrong or aren't entitled to a refund just throwing a different perspective out there.

EDIT:

Also as stated, you will have to get the refund yourself to your own account since you bought the game. If you get the refund they will then remove it from your sisters account I believe. Also make sure your providing the video and other evidence to GOG support.

Im just gonna jump in to defend Falcom games published under Xseed. Unlike Gurumin those dont have any game breaking issues so dont let a bad publisher like Mastiff stop you from enjoying good games. That is all :)

More on topic, i myself never have had an issue with gog support. There was this one occasion when my achievements disappeared and they fixed it near instantly. so to OP: Like others have said insist and provide all evidence required and im sure they will grant your request.