how can I play a game that isn't in the origin store?

I bought FIFA 12 two years ago on Amazon, as a disc. When I installed it, it went through Origin, and now I play the game with Origin. Now I want to get FIFA 13 or 14, and they don't show up on the Origin store. I found this that offers a FIFA 14 Origin key, but if the game isn't in the Origin store, can I still download it?
I've noticed that when I want to reinstall my copy of FIFA 12 I can just redownload it from Origin, so presumably it's somewhere in the cloud. Does that mean that FIFA 14 is also still around, but Origin just doesn't offer it in their store anymore?
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Can you add non Origin games to Origin?
When you buy a digital version of a game or downloadable content (DLC) for a game through Origin \u2014 either from the Store tab in the client or on origin.com \u2014 it's automatically added to My Game Library. You can also add games you buy outside of Origin, including physical games.Can you add games to Origin?
As Ivrognard mentions, Origin is needed. It's used for account management and ownership verification. If your concern is playing your games offline, you can choose to Go Offline within the Origin menu. You then shouldn't have any issues if connectivity is a potential problem area.Do all EA games Need Origin?
What happened to Origin Access Basic and Origin Access Premier? They just got a name change, now they're EA Play and EA Play Pro. You still have access to all the great games and benefits as an Origin Access Basic or Premier member.What Games Are Like For Someone Who Doesn't Play Games
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Images: Ryutaro Tsukata, Eren Li, Eren Li, Derick Makwasi