I suspect that you haven’t configured your page to go public.
To confirm, go to “Edit Game”. On the very bottom there are some radio buttons below the title “Visibility & access”. “Draft” means the page is only visible to you. “Restricted” means you can authorize people to view your page (usually to show your work to reviewers/friends before it’s published). “Public” will make it visible to everyone.
Massive warning: If you set the game’s page to “Public”, everyone on the internet will be able to see it. Make sure you’ve finished working on the page before selecting this choice.