Amazon prime gives away occasional GoG games. But for some reason they don't make the game as owned in the actual site.

You will see the game in your collection, you can download it and play it without issue but when you go to look at games to see what is on sale, it doesn't mark it as you owning it and you can't filter them out as owned games which sometimes has you staring at a game on sale with you swearing to yourself that you thought you already owned that game.

Anyone know why GoG has it setup like that and any chance of them addressing it so claiming a game from amazon still marks you as claiming that game?

I got couple games from Prime and they filter out for me.

In short, games obtained from Prime often have different IDs on GOG that the same games if actually purchased on GOG, so while the actual content of the package may be the same, what's in your library isn't, as far as the system is concerned, the same product you see when you check the game's GOG page. Why that's the case, no idea, but may have to do with the system used to allow GOG games to be purchased elsewhere.
In terms of fixes, they never fixed the issue that causes the elements that make up a higher tier edition of many games on here fail to show up as owned if you own said higher tier edition, so I wouldn't hold my breath about fixing something with an external cause... Well, not unless Amazon would somehow demand it, I guess.

Not me,

Elder Scrolls 3 and 4, I own them both but still shows up as unowned on the main page where you make purchases. Same with Fallout 2 and Fallout Tactics. Understood, won't hold my breath but I really hope they fix both of these. Especially with how they just inked an agreement with Amazon to work with Luna so I wouldn't be surprised to see even more games show up on their prime page.

Yeah, seems like Bethesda games are, ahem, prime suspects here, the fact that owning any of them on GOG also adds Arena and Daggerfall to your account likely having something to do with it, if there are extra hoops to go through in that situation if they're obtained elsewhere.
I see that Morrowind even has an appropriately titled package: https://www.gogdb.org/product/1432185303 (regular one is https://www.gogdb.org/product/1440163901 )

Fallout: New Vegas from Prime is a (one item) bundle that contains the game.

Everywhere on the store it says that I don't own NV until I get to the checkout page which correctly states “Please note that Fallout: New Vegas Ultimate Edition is already included in Fallout: New Vegas Ultimate Edition - Amazon Prime which you own.”.

That seems to be the common issue and it's very annoying that they don't bother trying to fix it. Fallout 1/2/Tactics have an additional issue – they were removed from the shop and later re-added as new games.

I've got everything except FO3 here and only FO4 (and FlatOut – thank you search function) is marked as owned.

This is different for each game. This problem is not isolated to Amazon, this is just a very old packaging problem at GOG. I have several pages of games I bought from GOG, not being marked as owned.

True, and that is very annoying :-|

when they fix taht, if I have a game in library i want to see that in shop too.

Anyway from today you can grab Fallout 3

Mine (Call of Jaurez: Bound in Blood) shows up on the site as owned by me, but it doesnt' show up on the app so I have no way of downloading it and playing it.

Download and install it via browser, and then see if Galaxy recognises the game then.

I would guess it's because in the case of cancelling the activation, for whatever reason, it has to be a separate entry and not identical to games purchased from GOG.

An extreme example case which is probably never going to happen:
they can probably deactivate all Amazon activations of some game with a few clicks, whereas if the game ID is the same, they would need to have some script searching through payment methods to separate how each user had activated the game.

It's of course a good question why doesn't the "Amazon ID" mark the "GOG ID" as already owned, at least in what is visible to users, they could be separate things internally.
But as all those deluxe edtions and DLCs don't do that with any other games either, it's just usual GOG database glitches, I guess.

I was finally able to find it on the website where I could download it. THANKS!

Just got Prime myself, via a free month trial, so jumped on the chance to claim some free games.

In case anyone else finds this thread, it is also worth noting that the Extras/Bonuses are missing from the games claimed via Amazon Prime.

True, from a certain point of view. The Prime games are normally base games, not complete nor deluxe versions with all available optional DLCs and artbooks etc added. But these aren't unique Prime "versions", it's just they're offering the cheapest edition of the game found on the GOG platform.

This isn't unique to prime though. Most platforms which offer giveaways often only give out the base game in the hope you buy the extras yourself. It's the way things are done, really.