I don’t exactly keep up with current video games, as demonstrated by my only recently finishing the main story of this game from 2017. Spoilers if you haven’t finished it yet yourself.

Should a game have a story? Can a game be a story? It’s difficult for a video game to present more than a scripted series of scenes. The player moves through them, in a fixed order, until reaching a predetermined ending. It is an experience much like watching a movie with narrative scenes interspersed by gameplay. You observe a story, without much agency in how it unfolds.
Many games today move beyond linear play structure by offering a “sandbox” or “open world.” The player travels about the game world, exploring and experiencing it as a place of adventure, battles, and puzzles. There are goals, missions, and quests to take on, or one can just play and discover all the interactions that the game designers have built into it, as if it were a big toybox. The Legend of Zelda: Breath of the Wild (abbreviated as BotW from here on) is an open world game in that style. So what does that design concept mean for a game’s potential as a story?
All the gameplay in BotW, which includes not only fighting monsters, but collecting mushrooms and butterflies, cooking recipes, riding horses, and many other activities, takes place on the background of a rich storyworld. BotW uses a classic heroic fantasy premise: an ancient evil, long imprisoned, has awoken to threaten the world. A hero must arise to defeat it. J.R.R. Tolkien set up this template in Lord of The Rings and it has been used countless times since in fiction and video games. In BotW, after 10,000 years of imprisonment, the great evil, Calamity Ganon, begins to spread its destruction, corruption, and chaos. You, the playable hero Link (I’m going to be saying “you” often for Link, since the game puts you in his narrative perspective), starts game play in a healing chamber, with no memory of your past. The large scale structure of the game is built on your need to remember that past and prepare yourself for the coming battle to save the world.
One of the first things to learn is that this apocalypse actually started a century ago. A group of heroes — the Princess Zelda, yourself, and Champions from each of the different folk of the land — conceived a complex plan to attack, weaken, and ultimately destroy Ganon. The plan was put into motion — and went very, very badly. You, Link, were severely wounded, and needed 100 years of healing sleep to recover. The fate of Zelda and the Champions is uncertain.
Over the course of the game, where your adventures have the goal of recovering your strength, special skills, and weapons, in order to try once again to defeat Ganon, you learn more and more about what happened 100 years ago. You talk to people who know it from legends. You find records and hear ballads and songs. You even meet people who are old enough to have been there when the past events took place. You begin to fill in the details of what happened and, in what is narratively important, of your past, personal relationships with each of the Champions. And what existed between you and Zelda. The complexities of that are presented through a set of twelve memories of significant moments that passed between the two of you. You recall these incidents by visiting the locations where they took place, 100 years ago. Find the right location and a short flashback scene plays.

The storytelling in each of these short movies has three different narrative functions. First, they tell a chapter of the preparations for the expected awakening of Ganon. You also learn the tragedy of Zelda’s life as someone caught between having been told she was born to wield a sacred power, and a growing inner doubt about herself, as she repeatedly fails to meet everyone’s expectations, those of her father most of all. Finally, each scene depicts an important interaction between Link and Zelda. Rather than a simple romance, their relationship is one that developed, changed, and matured over time. Link, in all the Zelda games through the years, is classically taciturn. We don’t ever actually hear his voice. Much of the complexities of his inner life are hidden from us. To understand him, we are left to consider why these particular twelve incidents are the ones that linger in his broken memory. Some appear trivial, innocuous, such as being with Zelda as she researches the botanical properties of rare flowers. Yet they are the ones that hold particular significance to Link. They are the embodiments of what Zelda meant to Link.
All of the game’s sources of information and history are encountered by choosing to go to particular locations or perform particular actions. Most significantly, the order in which you hunt down the memory triggering locations is left up to you. Some deliberate game design choices do influence this, for example some of the most important memories are triggered in locations that are challenging to reach, so you are most likely to achieve them latter in the game. Nothing forces that on you. You could seek out the challenging memories first, though successfully reaching them requires more skill at the game.

You learn of events, see personal encounters, and uncover secret dreams and fears in whatever order you come across them. You might first remember scenes of Link and Zelda as close companions, and only later find out that when they first met, Zelda resented and was jealous of Link. Then there’s a heart-breaking scene of a desperate escape through the pouring rain and Zelda, battered and blood stained, sobbing in anguish at the disaster and the deaths of the Champions, all of which she blamed on herself and her own failings. And only after that you might recover glimpses of Zelda struggling with the burden of her “destiny” in the coming battle with Ganon, a destiny she fears she will never be worthy of.
It makes for a very different experience than just passively sitting through a movie, or the linear scripted sequences in the story mode of most games. You as a viewer are having to do some work to assemble the pieces and see the larger structure and emotional framework. I felt in my play-through that my ultimate goal wasn’t so much to “save the princess from the monster,” but to help Zelda realize that this all wasn’t her fault. The events of that story might be as scripted as a movie, but the emotional experience is shaped by the circumstances of the play experience, as the player makes choices and interacts with the world of that story. For me, this involvement, this participation in the construction of narrative, makes me feel more involved in the events, more a part of them, rather than just being a passive recipient.
The narrative intent of the game’s creators does appear after you have recalled all twelve memories: a thirteenth memory becomes available. Recovering that unlocks a scene that explains and resolves a multitude of plot lines and emotional arcs. Clearly the creators wanted this scene to be a climax that rewards all the gameplay effort it took to achieve it.
Breath of the Wild, as a game, is about exploration and discovery. There are plenty of other typical video game activities, such as fighting monsters and dexterity challenges, but the mastering of those tasks themselves come from things you discover and learn about how the world works. Experiencing the narrative of BotW, rather than just being passive viewing between periods of game play, also arises from exploration and discovery. Game and story are constructed out of the same core activity. And just as the gameplay provides choice about where you go and what you do, the narrative as well can be engaged with to the degree that a player personally finds interesting. Some gamers have little interest in, or patience for the “story” parts of games, and skip past the narrative scenes when possible. YouTube is full of videos of players attempting challenges such as immediately going straight to the final bossfight with Calamity Ganon.

A video game can be a powerful story experience. Some of the most memorable games I’ve played, such as 1990’s Phantasy Star II or 1997’s Final Fantasy VII, I recall as stories I’ve experienced as much as games I’ve played. As game technology improves (and as movies allow more and more fantastic visuals), using games as a ways to tell stories is most successful when the creators try innovative approaches to narrative, rather than imitate how movies do it. See my series on what Pokémon Sword & Shield attempts. The plot of BotW’s story is still linear, with a fixed beginning and one ultimate outcome. It is the experiencing of that story which interacts with the game, and the emotional effect is shaped by your choices. The interweaving of free exploration and discovery into both the gameplay and the narrative is one of its great achievements.