I tried downloading the free game "Jotun" some days ago, but it didn't show in my library.

That wasn't the first time I couldn't "redeem" a free game from GOG, has happened many times before, is it just me or anyone else?

If you clicked on the banner when the offer was open it should be added to your account. Open your browser, login to your account and goto your library, it should show there, you might need to do a refresh. If its still not there contact support. I already owned it so got a key via email (you should get an email to notify you that it was added, if you didn't...) I donated to someone.

You can only download a game AFTER it's in your library. ;)

Did you click the "Get it now!" button (or whatever it said) on the giveaway banner on the front page? That was the only way to get the game. If you didn't click the button on the banner, you didn't get a copy; if you DID click the button, the banner should've changed to a message saying something like, "Your game will be added to your account soon". You should've also gotten an e-mail mentioning a free item being added to your library. If you got this e-mail, but didn't get the game in your library, contact Support.
If you didn't actually click the button on the banner, you're probably out of luck this time.

Just clicked on the game-page :S

There were two ways to get the game. The other one required more steps, though.

That's different from what they usually do -- normally, the "add to cart" button on the product page is either disabled, or it redirects one to the front page so one can click the banner.

That's unfortunately not enough. You should have clicked on "Get it now" on the banner, OR after clicking on the game page, "buy" it for 0$.

If you've missed it, maybe there will be some free codes floating around from guys who had it already.

worked perfectly fine here even on mobile

I got Jotun for free very easily. I don't remember exactly what I did, because I didn't even need to think about it. I believe that I just pressed a button or two in the GOG store, and then Jotun was added to my library.

this jank goes back to the beginning days of the site apparently, but only happens when I'm actually interested in a game, so necro