This can be accomplished using a General condition in the Validation rules of the fields you want to validate. Custom module objects are stored in the GlobalObjects macro collection, so you can compare the field value to the objects in this list.
For example, if the module is called Games with a class called Game, you can ensure that no Game has the same GameName with this rule:
!GameName.Value.EqualsAny(GlobalObjects.Games.ItemsAsFields.GameName)