If you edit the theme of a game, there's an options to put an image as a banner. I couldn't figure out where the banner for a game shows up on this site.

The banner only shows up if you scroll all the way to the top of a game's/user's page. Banners aren't used that much for that reason. As well as the fact that background images are used a lot more, which override banners. A good example of a banner being present somewhere is @baldnate's profile (Linked below).

https://speedrun.com/user/baldnate

What is a banner?

baldnate