Telling a story through gameplay is a subject I have thought a lot about.  It's funny because most narratives irritate me.  I have very high (or maybe particular) standards when it comes to a narrative oriented game.  However I'm going to talk about a couple of storytelling methods that I actually like.  One is more thinking oriented and the other is more feeling oriented.  I don't think I can be brief.  I apologize for that.  But I will try to be as clear as possible.

So, the first type of storytelling, the intellectual type, is simply making sure the progression of the game makes a type of coherent sense.  I especially appreciate this when there is no official narrative, no cutscenes, and little to no text explaining what is going on.  My favorite example of this is the Civilization games.  You start as a band of settlers, or pilgrims.  Over time you establish more cities, develop technology, expand your civilization.  There is a good chance you go to war, but you don't have to, and even if you do you can choose who to go to war with and who to ally with, including ally with no one.  Eventually there is a clear resolution to the game: you conquer the world or settle in outer space or something else equally impressive.  Or you might get conquered yourself.  All of the outcomes tell you the game is over.  At that point you kind of invent the storyline in your own head.  ("I did this, then I did that...eventually I conquered Aztecs last and won.")  The game even helps you at the end by giving a timeline of how things progressed.  This helps you invent the story in your head.  But the beautiful part of this story is that the details are different every time.  You chose every detail of how your part of the story would play out and then it forms a coherent narrative in the end.  

This can only happen if the game is structured properly.  The developers have to purposely structure the game so that it feels like it has a beginning, middle and end with a definite conclusion.  All of the individual choices in the game are the player's, but the mechanics are designed to make it feel like a story.  The beginning of the game feels radically different from the end.  This gives a sense of a dramatic change.  There are also significant, memorable milestones along the way, like you conquered this civilization or you built that wonder and so on.  The fact that few other games can do this shows how much effort the developers of Civilization put into making every part feel like it feeds into the whole narrative, even though it is a narrative you are creating in your head because of your own choices.

There are simpler games that tell the narrative purely through gameplay.  I especially like NES games, because they were limited in now much narrative they could intentionally put in anyway.  So a good example is The Legend of Zelda.  The official story is that you have to find the pieces of the triforce and use their power to defeat Gannon and save princess Zelda.  How well do the mechanics convey this?  Pretty well actually.  In the final dungeon you can't get past the first room unless you have all of the triforce pieces.  Once you have them, then you make your way through the dungeon, defeat Gannon, and in the next room is princess Zelda surrounded by fire.  You destroy the fire, and get a "game over, you won" type of message while Link and Zelda hold up the triforce.  So, the key quest of the game is really to assemble the triforce and the game makes you do that.  I normally hate hard gates to areas in a game like this, but in this case getting in the final dungeon tells you that you've completed the main quest of the game, so I actually like it.  The hard barrier works because it isn't just a gate barring access because of the developers wishes, but it is telling a story purely through mechanics.  Also you kill Gannon and free the princess from a type of prison, so that fits the official story too.  The only way the narrative could be illustrated better is if the triforce became an item that you could actually use against Ganon in the game.  But this is still the best example I can think of where a non-narrative game perfectly tells the scripted narrative purely through gameplay.

Another interesting example is the original Super Mario Bros.  This is an example where gameplay tells a different story than the one stated in the manual.  The manual says this, "One day the kingdom of the mushroom people was invaded by the Koopa, a tribe of turtles famous for their black magic.  The quiet, peace loving, mushroom people were turned into stones, bricks and even field horse-hair plants, and the mushroom kingdom fell into ruin."  It also says that the princess toadstool is the only one who can turn the people back and you have to save her from the Koopa turtle king.  How well does this narrative fit the gameplay?  Not too well at all.  Now, the gameplay actually does tell a story (see below), but it definitely doesn't tell this story.  The game rewards you for getting big.  Implicitly you believe that smashing blocks is a good thing and you have no idea that you are smashing people.  Also there is nothing that communicates the Koopa use black magic.  The turtles in the game seem like dumb animals instead of enemies intentionally out to get you.  Only Bowser and the hammer bros. really seem like enemies, and again, we never see them use magic.  We don't get any indication the princess can use magic either.  All of the magic seems to come from hidden items that you find: mushrooms, flowers, etc....

Instead the gameplay tells a different narrative.  The mushroom kingdom is a big place.  It has 8 worlds to it and each world has 4 parts.  There must be a ruler of each world, because each one has a castle.  You (Mario) are there to save the princess, but you have no idea which castle she's in.  Also you're really greedy because you are obsessively collecting coins.  The other rulers must be "toad" characters, because they are being held captive in the castles too.  So when you get to the end of a castle, they have to apologize, "Sorry but our princess is in another castle."  For some reason there are 8 creatures that look like Koopa kings.  Maybe they are brothers?  Who knows?  But each one is guarding someone in a castle.  Each one is trying to actively kill Mario instead of just walking around like a dumb turtle.  They do have spiky turtle shells, but given their size and fire breathing ability they seem more like Godzilla.  See in Mario's first game he defeats King Kong (Donkey Kong), so in this game it makes sense that he has to defeat Godzilla.

On top of all of this, what makes Super Mario Bros a great game is all of the other stuff that evokes the imagination.  I can invent other parts to the story that are even more subject to interpretation.  For example, why are their pipes everywhere?  In the Super Mario Bros cartoon they say Mario and Luigi were working on a drain and got sucked through a magic pipe, a valid interpretation.  However that is not what I imagined when playing the game.  I always imagined that Mario was dreaming.  Giant pipes don't seem to fit in a magical world of turtles and mushrooms, at least I don't think they fit.  Instead they make sense to be in a plumber's dream.  You go into a pipe and go underground.  It's like going deeper into his subconscious.  Also Mario is the only normal thing in this totally trippy world.  That is kind of what makes it work.  I couldn't get into Kirby the same way.  He's in a dream-like world, but Kirby is a pink blob.  Where is the piece of reality I can relate to?  But in Super Mario Bros, Mario himself is that piece of reality.  So I just picture he's dreaming.  It's an Alice in Wonderland type of world where mushrooms make you big.  Is Alice dreaming or did she literally enter a magical realm?  Often when this story is told, it's left to interpretation (but sometimes they just tell you).  Mario is similar.  It's suggestive, but it's up to interpretation if Mario really entered a magical world or he's just dreaming.

And that is the beauty of when mechanics tell the story instead of a narrative.  When it's done right your imagination takes over.  The story in your head is always better than an actual narrative, because your imagination is more active.  It's why the book is always better than the movie.  The book stimulates your imagination more.  Game mechanics mean you actually experience the story.  With a movie you empathize with the main character, but with a game you are the main character.  That is more powerful than empathy.  So if you play a game and then there is a narrative cutscene, you are immediately downgraded to watching another character and the game tells you that you and the main character are separate entities now.  It's not as powerful.

Anyway, this got wordier than I wanted.  This was all just my first point, the intellectual form of storytelling.  I don't have time here to talk about the emotional form.  Maybe I'll get to it later if you are still interested.

Yes even if you don't read much of the text you could see the interaction between he and his family before and after the incident, how much of a burden it was on him and also how often fathers take a bigger setback than mothers when a small children dies (and also how hard is for a marriage to keep after that).

Metroid Prime - Player can scan the environment at any time. These details make the entire story (other than the opening/ending cut-scenes or brief cut-scenes when Samus upgrades her suit/weapon/abilities or enters a new scenic area or encounters a boss.

For Example. There could be an alien science facility. There could be dead Aliens on the floor. If player scans them, each individual body has its own history of death. For example "head fracture from a projectile. Skull was recently at 300 degrees too". Then around the corner is loads of transparent containers, all but one of them have been smashed up. When scanned, "the containers where smashed from the inside".
When the player sees the transparent container that hasn't been broken. They notice a creature swimming around inside. When player scans it - "This creature was created by the Alien race (name of race) for the purpose of (purpose). It preserves energy from absorbing sound-waves. The energy is typically used to fire lasers at heat sources operating between (temperature range). This life-form likes the darkness as the darkness triggers chemical called which serves the same function as dopamine on Earth and can see in the dark".

Metroid Prime is a brilliant example of how to present an environment that makes the the player naturally put the story together by exploring and scanning the environment with a scientific visor.

Perhaps there are more active and less active ways of conveying a story through gameplay.
Less active could be anything that is transported, as long as you retain control over your charakter (like being able to walk around and look at the wonders of the game world).
More active could be anything that is transported specificaly through and because of your inputs, or somerhing that requires a response of some sort of input (like pressing R1 to hold Yordas hand in Ico).

But there is another way if thinking about it, when we look at the more active ways I just described: It feels dependent on the generality of your input. When you have a hand-holding-button, this is just what happens when you press it. That seems different to me than say clicking through a menue to find immediate commands for Civilisation (I use this as an example because it has been brought up and I find it extremely interesting to ponder the storytelling capabilities of a game like that).

What makes Civilization story telling through gameplay is how it directs the game play over the course of the game. It even had global warming already from the first version, rising seas and desertification if you didn't clean up pollution. That directed game play with clear beginning, middle and end sets it apart from other management sims like Sim city and Tycoon games. By playing the game [Civilization] you advance the story.

Brothers, a tale of 2 sons uses game play mechanics as well to tell the story. Perhaps it's mostly a staple of adventure (like) games to use game play mechanics to tell the story. Action games mostly resort to cut scenes, as well as RPGs and you often feel disconnected between what you are doing in game and how the cut scenes portray your character. The Tombraider reboot is a big offender of this where the game play is almost opposite to the story.

Working together provides good opportunities for story telling through gameplay. In the The last Guardian you get to know about Trico by working together. Your actions determine what he does, which is a great tool to learn about Trico and develop a relationship. Of course it's only the middle of the story that gets told this way, the beginning and end are through cut scenes.

The ainu game about the girl and the dog/wolf also do some storytelling through the gameplay. Never Alone, and it is a great game. There is one also that you play as a matroska doll

That is a cool take. When I think of a story it is mainly about interactions and inner workings of people. But who is to say that story cannot be something on a grander scale, albeit less personal. Civilisation might be able to tell a sort of story that is only possible through games. Pretty cool, very different from my thinking about story.

And it is so on point that you bring brithers up. I wanted to write about that game anyways. One half of the controller is for one brother, the other controls the other brother. There are spoilers of brothers in the next paragraph.

SPIOLER SPOILER SPOILER SPOILER

One of the brothers is gone and the other cannot swim. There is a body of water you cannot get around. When you try to do it with the half of the controller that belongs to the brother who cannot swim, it does not work. But when you try with the buttons of the brother who is gone, the younger brother overcomes his fears and swims.

END SPOILER END SPOILER END SPOILER

This is a huge moment for me. The narrative implications of the mechanics used are vast. I get shivers just thinking about it. What a moment.

What makes it even better, is that the game dies not teach you to do that. You have to think like that, obercome that hurdle, rising to the occasion, mirroing the brothers state of mind you control.