Gaming as mentioned before is many things to different people, and it is where these ideals intersect where it is possible to use gaming as a medium for cultural representation. Now that we know what can entail a cultural offering in gaming, the real question that needs to be asked is, how this can be achieved. There are obviously a multitude of ways that one can go about making games culturally significant, without being a blunt object to beat you over the head with the cultural queues. While also making it entertaining at the same time the cultural inclusion feels as though it is a part of the world that was created in the game.
There are a few games that include cultural queues that do it quite well, and the game series that comes to the forefront of my mind in that respect is the Yakuza series, or more specifically Kenzan, and Ishin. These two specific examples are due to the fact that not only are they showing, rather than telling cultural queues and ideas. It also includes historically important times in history, that are of course altered to get a story across, which is fine, because to make a period piece 100% historically accurate doesn't allow for creative interpretation,especially when you worry too much about accuracy, and not about fun, or game play.
Like mentioned earlier, the best way, I feel, is to make it feel as though the cultural integration feels natural to the player of your game, and is introduced organically which makes them feel as though they are included into your secret, and are that much more likely to be interested in more queues that increase their cultural interest, and knowledge. Of course if not done with the proper balance of subtlety and bluntness it can feel as though the people who may not notice what you are including without proper knowledge may feel as they are being left out of some sort of secret, and be less willing to continue. The best way to relegate this I feel is to include this in the most organic way possible, whether that be through mini games, or side stories. Yakuza Ishin, and Kenzan are especially good examples for this idea because the stuff that the side stories and mini games included have subtle cultural clues if you have the desire to read into them. If not then they are still fun mini games, and the side stories are interesting insight into the game world, and its characters.
This idea is not in any way saying that games as escapism or entertainment have no place, because that is patently false. However I feel that gaming can and should broaden its horizons culturally, and its also untrue that these ideals should be separate, if anything with what was said above, this should be more of a suggestion of coexistence in order to make a better mesh between these ideals. This is of course not something that should be exclusive, to the U.S, Europe, and Japan, but include every country that has or will make games. Because with proper integration within gaming as a whole, culture can be something more than just a 'members only' club for those people who live in the country of origin. If culture is shared, and understood by as large a group outside of the physical borders, that leads to the possibility of understanding more thoroughly things previously foreign to us. Once you broaden horizons it is that much easier to allow yourself to be open to new ideas, and realize, that as a Human race, we are not as different as people would like us to think.