The most part of our culture (both occidental and oriental) is based on storytelling, probably due to a tendency of the human nature, and because it's one of the best way to preserve and to hand down knowledge. We have told and still tell stories with every media at disposal. And games certainly are no exception. However since the medium is still young some differences are quite notable, differently to cinema, music and others, video games haven't still a specific language.
Each medium develops a language based on its peculiar and constitutive element. These languages can't express everything in the same efficient way, but they allow to take full advantage of the characteristics and communicative possibilities proper of the medium to which they belong.
Literature, using words, can express almost everything, but while a photograph can be more efficient than a description, nothing can describe feelings and states of mind as precisely as creative writing. Music have notes, and only with them it can evoke every kind of emotion, and unleash imagination. Cinema, despite being composed by various elements, has its core in moving images, to the point that it can tell a story just with them (one of the best example that comes on my mind is the Italian film Le quattro volte).
Video games should develop a language based on their main strength: interactivity. Though, until now, the main efforts have been focused on the development of a more cinematic language instead. Of course cinema has refined narrative techniques that can, and should be borrowed by games, but it doesn't provide an answer to the problem of storytelling. And using cutscenes to carry on a story is quite trivial (and quicktime events are just a slightly better solution).
One of the reason for the use of a cinematic language in video games is probably to found in the difficulties to carry on a tale using interaction. Many argue that mixing story and interactivity destroy narration: how can I tell Little Red Hiding Hood if I give to the player the choice to not going through the woods?
Interactivity is an entirely new factor in non-verbal communication and other media doesn't really provide it, so we don't have a tradition where to look for. But we aren't totally clueless, to understand how it can be used to enhance the narrative experience, instead of destroying it, we have to change our point of view, and theatre can be a valid option. While a play is quite traditional in its way to tell a story, what is interesting it's how the actor realizes the narration. The actor is interacting with the space around him and with other actors: the story is told by her interactions and actions.
This point is quite important because it says us that a story can be told through actions performed by the player, without the necessity to let her takes choices that influence the plot. Furthermore this way to intend interaction highlights how a player can be involved in a story just let her interpreting a well defined character.
Two problems arise with this approach: the actor isn't a spectator, and theatre isn't really based on interaction, but it takes move from literature, thus, from traditional ways of narration.
What interaction really changes in stories is the focus of the spectator. Movies, plays, novels, we watch and read them because we want to know the causes and effects of the actions of their protagonists, interactivity breaks this mechanism, if games put the focus on effects and consequences, they have to let the player decide about them, or to take completely off the control of the plot. Therefore narration in games cannot be based on cause and effect but on what stays in between: actions. People should want to play a game willing to perform actions and not for seeing their consequences. But beware: it's just a matter of where to diverge the attention of the player, and not to destroy the cause-effect relation.
The best way to achieve this kind of storytelling (that we can call performative) is to change the gameplay to suit best each part of the story. Basically all the FPSs, in a macro perspective, tell the same thing: someone that shoot someone (or something) else. Changing the gameplay means tell a more complex story, and to articulate the gameplay means to use it as a language.
Performative storytelling isn't totally new, and some of the best examples are two Molleindustria's games: Every day the same dream and Unmanned. Both tell their stories giving control to the player and let her perform the actions that compose the story. The first one doesn't even need to change its gameplay, but just with simple actions tell something much deeper than the average game.
Unmanned is a more complex example, its changes in the gameplay allow to describe with extreme precision the working day of a military drone operator. The design gives a considerable depth to the experience, providing the player with a narration that doesn't need cutscenes or too much dialogues, and, at the same time, that involves her with different and compelling kinds of interactions.
The debate about interactive and narrative revealed itself as a problem of perspective, if storytelling is considered as a consecution of actions instead of a cause and effect one, then interactivity can be used to enact these actions. Therefore not only the language of video games should be based on interaction, hence on gameplay, but also it's perfectly suited for narration.