To see a full list of the games in your library, click the "All Games" tab on the left side of the window. You'll see a list of every game you've claimed through the Prime Gaming program.
Xbox Games with Gold is a service that allows you to download fan favourite Xbox games for as part of your subscription. Since there's a new selection of games available every month, it's worth your time knowing which titles will part of the Xbox Games with Gold to ensure you don't miss anything exciting.
Do I get to keep the games I already claimed? Yes. This does not impact any Xbox 360 games you downloaded before October 2024. The Xbox 360 Games with Gold titles you've claimed are yours to keep on your Xbox account, regardless of whether you continue your subscription.
