Suppose we have a narrative we want to convey, and we want to do it during gameplay, but we decide to restrict the means we have to express it -- possibly by limiting it to a single type of media. Let's examine some different ways games have dealt with this type of situation.
In BioShock, narrative expression was frequently limited to the auditory channel, in the form of audio logs that the player would pick up and optionally listen to throughout the game. When narrative is limited to audio, it means that all of the other available channels remain open for communicating gameplay.
Since visual language is arguably the most important method of facilitating gameplay, this means that the player can apprehend the auditory narrative without much interference or limitations on game action.
As long as the audio from the narrative does not interfere with whatever audio cues might be crucial to gameplay, both the narrative and gameplay can live quite nicely alongside each other.
However, we find an important tradeoff even in this exchange. You cannot express the same things in the same ways in pure audio as you can if you also had control of the visual dimension. You only have volume, duration and tone to express the quality of an explosion.
You can't depict a character climbing onto the Hydra's head except by literal narrative account ("I'm climbing onto the Hydra's head!") There are all kinds of details that cannot be adequately expressed when your narrative is limited to audio.
Some games that also limit narrative to auditory information do it in the context of a character that is actually in the game to varying degrees.
In several of the Ace Combat games, narrative is conveyed to the player via radio communications from a special radar aircraft that is essentially uninvolved in the gameplay action, as well as from friendly and enemy aircraft that do engage the player directly.
This case is interesting because the game also relaxes the idea of how radio communication actually works in order to present a more compelling narrative. Regardless of friend or foe or radio source, you get to hear all characters' communications all the time. Unlike BioShock, the auditory narrative takes place in the present rather than from the past.
Elaborating on this theme a step further, In Call of Duty 4: Modern Warfare, narrative takes place in the form of an NPC soldier who operates alongside you, gives you commands, and warns you about the obstacles you're about to face. Because of this, the narrative is meshed with gameplay more tightly than in BioShock or Ace Combat, as now we have a visual, physical source of narrative in close proximity that actually performs in concert with gameplay.
Even in this situation, our narrative control is limited. Because the player has full control over the camera, we cannot author any camera work as part of the narrative expression. When you're engaging the enemy, you don't have much time to look at what your fellow soldier is doing. Call of Duty 4 tends to place more emphasis on listening to what your soldier friend says when there are enemies in your face, and then tends to emphasize the visual channel when there aren't.
Similarly, Half-Life 2 allows the player to stay in game perspective and control during cutscenes, instead of arresting the camera away. There are two non-obvious tradeoffs here.
First, the developer has to carefully entice the player to look in the intended direction so they can see all the action. This can be accomplished by limiting the view of interest by the inherent design of the physical space (If you're in a hallway, there are only two interesting directions to look in, and the player will tend to favor the direction they are already heading in).
Second, the game must establish a grammar of trust in the game world by not throwing in a crazy enemy who will backstab the player while he's watching two characters converse. Even though the interface is unchanged from gameplay scene to narrative scene, the player needs a hint as well as this consistency of grammar so they "know" their attention should be on a conversation instead of walking around the room's corners looking for items and enemies.
In either case, you can never guarantee that the player will actually view what they are supposed to.
From these examples, we notice that when narrative expression is restricted in some ways, gameplay can be expressed much more richly.