The question is: what type of artistic expression can games convey? The following is not remotely academic; I'm just organizing some thoughts.
The components of a game can be artistically rendered, e.g. a beautiful chess set or artistic landscape in a video game; games can be the subject of art, e.g. Death playing chess in The Seventh Seal.
Uninteresting. Not writing about that.
Interactive art is a type of interactive activity and a type of art. Some interactive activities are interactive art. Some art is interactive art. All games are interactive activities.
This doesn't imply that all or any games are interactive art, but some games could be.
What does interactive art convey that one couldn't equally convey using non-interactive art? Considering messages which can be conveyed with interactive art, such as tragedy, heroism, love, guilt, and so on, one sees that these can also be conveyed with the plastic and performance arts.
The usage of interactive art is a choice to portray something that could also be portrayed in other ways. This is true for all artistic choices. Like different languages, a particular medium may lend itself more readily to conveying certain types of messages.
As a choice, an artistic message can be conveyed though means of a game, which is merely an interactive activity with some constraints. It doesn't matter how we define a game: requires winners and losers, goals, rules, points, or what have you. Whatever definition we use, it is can be a medium within which to create art.
Suitability for Children
Anybody who complains that the message conveyed by a game is not suitable for children understands neither games nor art.
Games used to convey artistic messages need not be wholesome, fun, enjoyable, or even replayable, any more than messages conveyed through any other artistic medium. The notion that a game must enable flow or draw people into a zone, or anything other than exist as a medium is to conflate marketability with message.
Art should never be designed with marketing requirements in mind. Viewing an ugly painting that you would never place in your house is equivalent to interacting with a horrific game that you would never play for more than two minutes.
A game which provides flow and draws people in may be better able to convey certain types of messages, and perhaps less able to convey others. These messages are typically ones that are conveyed through repetition or narrative.
Winning Conveys Only Perseverance
At any point during a game where winning is the conscious goal of the participant, any other artistic message is necessarily excluded. This is because winning is not an artistic message of anything, other than perseverance.
All competition necessarily has a common experience, namely overcoming obstacles. This experience is independent of the particular game being played. Therefore, it is not useful in deciding if a game can carry a specific message unless we exclude the message of perseverance. Messages other than perseverance can also be conveyed by any type of competition, such as ethics and grace.
Winning is calculating and numeric. In a dance competition, where the winning dance is the most artistic, the dance is artistic, but the points and other aspects of winning the game are not. Remove the game, and the dance remains equally artistic. Remove the dance, and no art remains other than the message of perseverance.
Art vs Instruction
Art is different than instruction. Teaching about the Holocaust is different than experiencing art about the Holocaust, whether the art is a game, play, or painting. Any part of a game that is simply instructional is not carrying an artistic message. An artistic message is one which is understood without, or beyond, instruction.
Most "educational" games are simply "instructive", and are boring. All games are inherently educational, although some may convey unpopular messages.