Literary realism is narrative form of story telling in which the writer tries to depict reality through commonly occurring events in order to make a point about our own lives. This is a style which could be interestingly used by video games, but almost never is. Instead of trying to depict reality, video games will often try to be realistic (more often than not through violence, as in realistic violence, or visuals like those in Heavy Rain or Uncharted).
There are only a very sparse examples of realism I can think of for video games, and this may be because in an interactive visual medium where the possibilities are endless, not a lot of people may want to plow the fields or brush their teeth to find meaning, when they can go shoot space aliens for fun. But there are a lot of interesting things one can do with realism, without having to be 100% realistic that can be used in gaming and still be entertaining.
Likely the most popular game series to use realism are the Harvest Moon games, which have the player break logs, farm crops, buy seeds, and tend livestock. These games are no where near realistic, but they do represent the real struggles one is faced with in the life of a farm. Animal Crossing tends to depict the continuous life of debt a rural survivalist faces in the world of capitalism, though I'm sure that was never the intent of the game's creators. Both titles lack any violence and can often be termed "casual games," but are the closest a mainstream video game comes to realism.
Stop. Yes, these games feel more like realist works than things like Bad Company and Modern Warfare. Those game romanticize war, even in the death and brutality. They are not works of realism, in any way. The grandiose scale and extreme speed surrounding events, and the over-the-top conspiracy theory plots in most war games make great excitement, but lack the elements of realism which are most important. They could probably be categorized as romanticism.
A few examples of realism in gaming would be Desert Bus, The Graveyard, Pigeons in the Park, Snowdrift, and Home. These more fringe, independent (often freeware) games are more down to earth and realistic, showing daily activity, than most anything in the main stream.
Desert Bus is an old Sega CD game about traveling across the desert. It's played for laughs, by managing to be obnoxiously real. The game probably points out what many would believe about realist games - they would be boring.
The Graveyard is an extremely divisive game by the extremely divisive Tale of Tales, where you play an elderly woman walking through a graveyard. It's barely interactive, but the good intentions and the five dollar asking price for the game make it hard for me to honestly hate. Not to mention the purpose of the five dollar purchase is clearly stated by the creators. If you buy the five dollar game instead of just playing the demo, the only extra you receive is to watch your character die. It's a bizarre concept, but an interesting one. A neat experiment, really.
Pigeons in the Park (as well as many of the games) by Deirdra Kiai is a very realist game, where the player just talks to another person while sitting on the bench. It's pretty good. The conversation is very interesting and you get the chance to explore two very different people's somewhat fragile minds. Definitely recommended.
Snowdrift by increpare and Terry Cavanagh is a game about getting lost in a snowy wilderness, and you definitely feel lost during your time out there. I sometimes wondered if there was a chance to actually make it back home in the game, or if you were always destined to freeze to death. This also could be noted as a naturalist work, a facet of realism. There is nothing in the game that could not happen in reality, and it's well worth playing for a bit.
Home by increpare is probably my favorite of these realist games. Like The Graveyard you play as an elderly person, but the gameplay is interwoven with the narrative much more thoroughly. The character has to maintain his food, bowls, and other stats as his body slowly deteriorates and his mind dulls. It displays the helplessness and pain of aging perfectly through the medium.
Especially with the last three games mentioned, realism can be used really well in games. A developer doesn't have to make an especially realistic world, they just have to make a realistic scenario and integrate it well with the gameplay of the medium. Reality is hardly dull, and like most realist works in literature display, it can be very challenging. And challenge is one of the key elements in most games.
I'm curious to see the game Dinner Date in action, as it is exactly what a realist game may want to be: an experience of events in order to empathize with a person in a situation while still connected to reality. And the designer sounds like he has made some very encouraging decisions for the game, like the player control the lead character's subconscious instead of controlling his entire body. That may serve to add an extra layer of depth to play, and serve the medium properly.
We'll see if it can pull off being an exceptional game in an under-used genre in just a couple days.