The narrative experience is likely one of the most obvious types of experiences a game can provide. It is the exact same experience as a book, a movie, a TV-show and so forth can produce. You are being told a narrative. This might be through cut-scenes and dialogue, but it can also be through gameplay and the presentation of the game. The narrative experience of a game frequently overlaps with most other experiences of a game, and the best narrative experiences do not exist isolation. There are countless different types of narratives, but here are a few examples frequently found in games.
Power fantasies
The fantasy of power is one of the narratives that games can do in a unique way. While you can read about, or watch a powerful character, it is not the same as controlling a powerful character. This type of narrative is typically told through gameplay where you control a very powerful character that can decimate the enemy with ease. This is a very common thing in video games as it is often an excellent excuse to create good gameplay. This is not to say that the game is easy, but that the character you control is simply much more powerful than what is normal in the context of the game universe.
The character experience
When you care about a character in a game you experience a character driven narrative experience. You can love or hate the character, and anything in-between. As long as you feel something when something happens to a character the experience can be classified as a character experience. You can feel for a character when something happens to them, or you can want the character to die and feel a lot of satisfaction when something bad happens to a character you dislike. This aspect of experience works the same for video games as it does for books, movies and so forth.
World driven experience
World driven experiences are experiences that surround the world. How is the world and society structured in the moment of play? What is the history of the world, how did the current world come to be? What is the future of the world like? Any experience about the world, and curiosity concerning the world creates a narrative experience driven by the players interest in the world itself.
The thought provoking experience
Thought provoking narratives makes you think. They might bring up philosophical ideas that you are unaware of, or does something very unexpected that leaves you heavy in thought. What is the meaning of life? Why do you think the way you do? How do you know what you know? What is right and wrong, and why? These are questions thought provoking narratives might try to make you think about. The experience of pondering questions like this can be quite profound.
Theme based experiences
A narrative can explore a theme. How does slavery for example work, why do people go along with it? What are the benefits (economical ones clearly) of slavery versus its costs? How does slavery impact people, both directly and in-directly? How does slavery get introduced in the first place? How does it end? There are lots of questions you can ask about any theme, and you can tell a very in-depth narrative about almost any theme. The theme can also be used as a springboard to dive into other themes and concepts; how does the slave owner justify slavery to himself in his mind? What does that tell you about himself, and by extension humans?
The overarching narrative experience
A lot of these narrative experiences are frequently combined together, and they can be stacked on top of each other to no limit. The important part about the narrative is to know the focus of the narrative to prevent it from growing into an uncontrollable beast. It is very easy to include too many things into the narrative, which leads to a mediocre and low quality narrative. No narrative experience happens by itself, it needs to be built up from a foundation and nourished throughout the players experience before it can flourish. You don’t get a good character experience if you kill a character no one cares about. You need to do the foundational work to set up every single narrative experience you use.
There is a lot to be learned from traditional mediums such as books, TV and movie production. Good characters are the same in video games as they are in any other medium, they are real believable people. Good worlds are the same, they are consistent within their own established rules. How movies use camera angles, camera distance from the action is very transferable to narration in video games as well. Writing well is important in books, and the same rules applies to video games as well. A lot of the foundational craft of narration and storytelling transfers heavily to video games.
The extra element video games has to enhance a narrative is player interaction. This can be gameplay, player choices or simply having the ability to walk around in an environment at their own pace. These elements are chances to improve the narrative, but they are also a potential mistake and source of narrative dissonance. What the player does and sees might not be what they are being told in a narrative. Merging gameplay and narrative together into a good mix is quite challenging to do, but is in my opinion also how the greatest narratives in games are created.