If I get a game from the Apple store, can I play it on other computers?
If you purchased the game from the Mac App Store or iOS App Store, you can download it on other computers signed into your Apple ID.

On the Mac App store, click on the "Purchased" tab. If you need to sign in, sign in with your Apple ID. Then if you purchase an app, it will be attached to your Apple ID.

Then you will be able to redownload apps or games you have purchased with your Apple ID.