In a game we're often forced to pick between wishing whether it had a better narrative or better gameplay. But you know what, why not just settle for a game that is purely narrative, forget gameplay or keep it to a minimalist aspect, you can always just enjoy a game that's mostly to entirely story.
Telltales Games literally made a company out of this and made bestsellers that are basically just TV show episodes as games. Even before that, the Japanese took the concept of visual based storytelling and sold them as visual novels. Heck, some of the original video games were choose your adventure text games, where you'd get text descriptions of a game, and input in basic commands to guide your way through the story. Colossal Cave Adventure (the first ever text adventure game) actually still exists online as a free to play open source game.
What makes these games stand out is their general emphasis on favouring a story over actually making you play a game. Now while some people do like min-maxing their custom RPG characters, or enjoy their shooter campaigns or whatever, some people prefer a casual relaxed game that doesn't take as much effort to enjoy.
Visual novels are perhaps the most popular format for a narrative based game. Primarily made by Japanese developers, it's easy to overlook them as just another part of the “anime culture” for the lack of a better phrase. They usually are mostly text walls and sprites for characters talking, sometimes with voice dubbing over the lines, and 'event CGs', which are special graphics that appear when an important event/scene is triggered. While usually they're branching stories, many are linear too and just exist to tell a straightforward story. The Fate franchise and Steins; Gate are both extremely popular visual novels (the former having more text across all 3 routes of the original game than Lord of the Rings, let that sink in) that are often recommended as great entry points for people trying to get into the genre without wading through the dating sim plethora that plagues it.
Even more recently, Doki Doki Literature Club made waves for being a psychological horror game disguised as an innocuous looking dating sim visual novel. Despite being made in the west, it was still a great example of how great the visual novel narrative can be used to tell a story. Games like Emily is Away are also similar to visual novels, taking place in mostly contained text stories with minor interactive features.
Telltales' format for point and click adventures, released in an episodic manner much like a real TV show also made a huge push for narrative games being popular. Each episode of a game told a story, and offered choices for players to immerse themselves in the story and feel like their actions mattered, although it'd be still fairly linear as the plot would ultimately end in the same direction, with your actions having minor consequences in hindsight, something that Telltales is often criticized for. Dontnod Entertainment's Life is Strange also followed a similar episodic storytelling concept, with a lot more interactive gameplay other than simple point and click and quick time event button mashing and definitely more consequential choices for a player to take.
Walking simulators are even more diluted in terms of gameplay, hence the on-the-nose name implying all you do is walk around. Firewatch was an incredibly moving experience and visually stunning thanks to the art of Olly Moss contributing to the game. It made great use of a beautifully designed real life setting (a wildlife park) and a fantastic interaction dynamic between the player-character Henry and Delilah, whom you never meet but talk to over a radio. The great voice acting and immersive atmosphere helped sell the game really well, and kept players invested all the way till the very end despite the game really just being mostly 8 hours of walking around a forest, albeit a really beautifully designed one. The Stanley Parable is another walking simulator which originally spawned as a Half-Life mod, which is widely praised for its inventive narrative style, which veered into some really meta territory and also offered branching choices for a player to take, with multiple endings present in the game. The very structure of the game makes it great for how philosophical it gets with the medium, and makes great use of having no 'real' gameplay to tell a story.
Ultimately, narrative games are fun because they choose to capitalise on using video games as a medium for their storytelling. While they can go the easy route and just tell a straightforward linear story, props to branching story games that force the player to think about what they're playing, and make often hard choices that force players to think about a story and unlike novels or other traditional games, feel like they are getting more out of the story by having a direct hand in it.
Narrative games are great and should not be overlooked as much as they do for not being like traditional games. Give it a try; you can't really go wrong with a good story.
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