Wanting to download game onto a second device

Are you sure you are in the Origin account you first installed the game with?

Try these:

The game no longer shows up in Origin

Try the following things: 

• Restart Origin.
• Log out and back in and use the email address instead of the user name. Make sure to use the one you used to register the game in the first place.
• Reinstall Origin.
• Restart your router/modem.
• Make sure the game isn't hidden by accident. To check, put the filter to Hidden Games. If it's there, right-click on the game to unhide ((click on the spoiler below to view an exemplary screenshot))
  
  Spoiler
• Get in touch with an EA Game Advisor.
  
  Source: http://answers.ea.com/t5/The-Sims-4/FAQ-Serial-Codes-Game-Activation-and-Download-Issues/td-p/4228232

you should be able to reinstall it on your other device by following the steps below

1. Go to the Orgin sie and login on you other device that does not have that game

2. go to your game or purchased and find the game

3. Finally reinstall the game and you should be able to play it

Hope this helps 🙂