Welcome to the Q&A Forum

You can supply ratings for the following content types:

• Book
• Course
• Event
• How-to
• Local business
• Movie
• Product
• Recipe
• Software App

Google also supports reviews for the following schema.org types:

• [CreativeWorkSeason](https://schema.org/CreativeWorkSeason)
• [CreativeWorkSeries](https://schema.org/CreativeWorkSeries)
• [Episode](https://schema.org/Episode)
• [Game](https://schema.org/Game)
• [MediaObject](https://schema.org/MediaObject)
• [MusicPlaylist](https://schema.org/MusicPlaylist)
• [MusicRecording](https://schema.org/MusicRecording)
• [Organization](https://schema.org/Organization)

Check the definition of Game, I think in your case it should be a Organization type.

Original post credit: https://support.google.com/webmasters/thread/14697981?hl=en