How to install previously purchased game on new computer

I'm not sure where to ask this since it's more of a general question. We bought Sims 4 in 2020 for my daughter, but she was a bit too young and struggled playing. Now that she's older, she wants to play again, but she has a new computer and I'm not sure how to install her original game on her new one. This is the account she used, but the game itself we purchased on Amazon (they were having a half off sale due to covid). I still have the product codes, but I'm not sure if they would work on a new computer or if it would say the codes were already in use. Any thoughts or advice would be appreciated!