I know I can hide it, but can I delete it so it cannot count as a game I owned?

No.

Theoretically technical support could, but this would be a huge waste of their time that could be better spent fixing actual technical issues, so they're likely to refuse to do it.

In most cases, that would be true. But in Gwent's case, it's best to get the cancer excised from your account entirely so they don't try to count you among its numbers.

So my problems dont matter for them...

They won't even delete achievements or played time. I doubt they'll remove the game. They need every single byte of your personal data to feed their families. The only winning move is not to play.

What's your problem again..?

I'd say that if your problems are solely that you're upset that you've got a free game in your account and that merely hiding it from view isn't enough for you, then I'd say no, it doesn't matter to them.

Think of it this way - is it better for a support technician to help someone who actually wants to play a game he purchased with his own money, or should he ignore that user and spend twenty minutes deleting a game from your account that quite frankly you can just hide and ignore?

I don't think it'd take 20 minutes to delete the game from his account. They can probably do it with a couple of clicks.

They could. But they probably don't want to. Considering how desperate GOG has tried in the past to push Gwent and it's Micro-Transactions on everybody, they won't willingly remove it from anyone's account who fell for their push and accepted this 'free' game.

Well I think you can (and should) at least try. I sure would if I ever added that shit to my account
Just make a new support ticket
https://support.gog.com/hc/en-us/requests/new?product=gog

to avoid the stupid bot you can use this userscript:

// ==UserScript==
// @name Gog Do not bother with stupid bot
// @namespace NotStupid
// @match https://support.gog.com/hc/en-us/requests/new
// @grant none
// @version 1.0
// @author LiefLayer
// @description 14/12/2022, 17:01:33
// ==/UserScript==
document.querySelector('div[data-default-form]').setAttribute('style', 'display:inline !important');
document.querySelector('div[data-chat-wrap]').style.display='none';
document.getElementsByClassName('row clearfix')[0].classList.remove('is-hidden');
document.getElementsByClassName('post-form-message')[0].classList.remove('is-hidden');
document.getElementsByClassName('new-request-form')[0].classList.remove('is-hidden');

PS. I also suggest this
https://www.gog.com/forum/general/adalia_fundamentals_fixing_gog_so_you_dont_have_to/
and this
https://dawedhel.github.io/Barefoot-Essentials-Fork/BE.js

Its NOT a free game. Its a free to play game and I dont rememer how it ended up with me in the first place.
Maybe when I joined and I clicked whatever, which according to the info was 3 years ago already but havent used nor buy a game from this site until now.

It sucks! And my problem matters!
Steam (well of course, Steam!) actually allows me to permanently delete even full paid games.

I dont like that shit counting as a game I own.
And they havent responded my ticket support, and probably they wont.
But officially they havent due to high demand if their latest email is to be believed, but its hard to believe since they are not Steam, they are not even EGS and according to the info from some of you, this is way older than EGS??!!

Anyway, it sucks!
What the hell are you doing? the problem is not reaching them. They dont respond. I just have emails saying they will answer soon but nothing.

There would be a load of validation to go through and controls as well. 20 minutes might be a bit on the high side, but the point remains that it's a waste of support's time.

Look, you didn't pay for it, so as far as I'm concerned, it was free. Your lesson here is that if you can't stand having something in your account that you don't want, don't claim free stuff. If you really can't cope, open a new account, but obviously, because the site is DRM free, you're not able to transfer items between accounts to prevent abuse.

I'll agree with you that you believe that your problem matters and leave it at that.

They will respond eventually. Just give them a few months (no, I'm not kidding, I tried multiple times, they will always respond but they need months to do it).
It was not like that years ago, but right now I think their support team is too small for a website like gog.

Even if they delete it, your count might still be off. Mine has been off for a while now. Mousing over my account name shows I have 1,753 games but I have almost 30 more than that. That's not even counting the demos.

haha wtf.
What a joke!
I wont leave it at that!. I found distasteful your POV´s.