Games does not collect any of your data. The only data the app stores are your settings. These are only saved locally. No one, other than you, has access to this data.
When enabling iCloud sync, your list of games in the library and wishlist along with the data you've provided (including custom images) are stored on Apple servers. Games does not have direct access to this data.
For analytics Games uses TelemetryDeck in order to collect information that can help me make better development decision. You can turn off analytics via Settings > General.
If you have any question, do not hesitate to send us an email at firstname.lastname@example.org