EDIT: You can check if a game would activate game mode by locating the application in finder (I’ll use NMS for this example which can be found at ~/Library/Application Support/Steam/steamapps/common/No Man's Sky.app. Once you've found it, right-click and choose "Show Package Contents", select Contents, and then open Info.plist in whatever text editor you have installed (TextEdit works just fine) and search for the key ApplicationCategoryType. The line under that should say something like
public.app-category.games. If it says that then it will activate game mode. If it says something else or there isn't an ApplicationCategoryType key, then game mode will not activate.