We don't really have a standard way to do it - it would be best to keep all the games on the same page unless they are significantly different for some reason. So I would say...
- Same entity with only slightly different game-specific stuff -> add info box with the game-specific info
- Same entity with very different game-specific stuff -> create new page with the game-specific info (new page called "entity_name (Game Name)")
Basically if the info box has a lot of text in it, put it in a different page. And then optionally on the page for the base entity, you can add an info box with a link to the other page for the CSDS users.