Now before I begin I am going to say I am excluding games with heavy narrative focus as well as RPGs in this. It isn't so much that they don't have good stories, it is that they often do but in a way that is pretty difficult to ignore. You can talk about them, but for the most part they don't contribute to the issue.
Instead we are looking at games where typically the stories are often lampooned as universally terrible such as Fighting games, Platformers, Action, strategy games and what have you.
The question is really can a story be considered good not "for a 'game of that type'" but rather be good because it is built for that exact genre?
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One genre of game I keep hearing over and over again as being "universally bad at story" are fighting games. Yet whenever I think of an interesting story my mind often goes right to fighting games.
Sure the story is usually dirt simple but it is every single character's individual plots, motivations, and history that usually bring them together.
I don't think the fact that fighting games MUST constrain themselves to that format makes their story bad. No more then a painting is bad because it is contained to a canvas. The story does exactly what its job is to do.
Just because it doesn't lend itself to a good novel or a good movie it doesn't mean it is invalid.
Strategy games show this in spades. If you were to convey the Command and Conquer games to a movie format they would be downright boring. Yet in terms of drawing you into each battlefield with an idea of the scope and importance of every mission it succeeds.
Alright, first of all, you can't ask whether or not video game stories are good and then say, "but don't look at the genre with the best stories." That's BS man.
Secondly, terrible stories are ALMOST universally due to production budget rather than writing. Get your hands on the scripts, many of them are top-notch. Now to follow that up with a genre-by-genre analysis, i'll point out that even "story-driven" games, RPGs, and MMOs can have bad stories. In fact, i'd argue that the TES series in general has rather lackluster storytelling on the whole. Alternatively, games like WoW can have really kickass stories. I'll agree with you on fighting games, but then we don't really play them for story. In fact, many of them fall under the sports game category where the point is arguably to create your own story so really, that just leaves games like street fighter and mortal kombat. When it comes to platformers you're dead wrong... DEAD. WRONG. Castlevania, Metroid, and Shadow of The Colossus come to mind. EVEN MORE IMPRESSIVE is that those series' wholes are greater than the sum of their parts, where they've managed to create pretty engrossing worlds and universes. Action is hit-and-miss, and the main genre where you find excellent stories ruined by budget. COD is a great example, especially MW, WAW, MW2, BO, and Ghosts... The writing is good... It just doesn't always make it in to the finished product. Look at Halo, that shit is amazing. Are you kidding me!?!? i'd actually cut my legs off if it meant I could be in the writer's room for Halo. Even 4. Guardians looks beastly, and the series as a whole is another example of a totally engrossing universe. It's beautiful. Also Batman: Arkham Knight is incredible, and the story is A+++. Finally, i'll give you strategy games... Especially during the early 2000s the trend was either minimalistic story or full-on camp. Lookin' at you NOD. That trend is starting to change, but strategy just isn't as big of a market as it once was. Halo Wars comes to mind, but much of the best fluff was cut (Mechanics too, you fuckers, I wanted my warthogs to jump cliffs solo badly.)
"can a story be considered good not "for a 'game of that type'" but rather be good because it is built for that exact genre?" ssssssssss, dude. No. There are stories, like them or don't. Also, every genre has not been explored or exploited to its fullest extent so it's kind of hard ask that question, and on a game-to-game level, there are "bad" games with great stories. Mass Effect, Advent Rising, Telltale stuff in general... The list is long. Good stories can save a lot of mediocre games. In short, other than time and budget, there's not a huge correlation between story and genre for me.
Back to fighting games... That's tough, and a genre that really blends in to many other genres. Toribash, street fighter, mortal kombat, UFC, Boxing, etc. Those are games I think universally considered to be JUST fighting games. None of them have an appreciable stories as far as i'm concerned.
I'll say that not all games which are fighting based have to be similar to the above format... There's the jedi Knight series, where once you get your lightsaber it basically becomes a fighting game with all the finesse and movement that can go into maneuver and attack. There's also the Arkham series, where fighting and action are blended. Both amazing games in terms of mechanics and story. I say, you're right in that the format of the game doesn't make the game bad, but it does make the story bad. The game is the canvas, and story is only one of the colors. Any story that's just doing "what's its job is to do" is a bad story. Story in games should drive gameplay and interest, and at times frustrate the player. The same is to be said of plot. Story should never just LEAD YOU to the next encounter. It should make you seek it out in either desperation or interest.
While i'll agree that video games are a different medium entirely and don't always lend themselves well to the pen or screen, story as a tool never works well. Stories are LIFE. You create them, and they go off and evolve, they invoke response and emotion, and most importantly they MEAN SOMETHING TO YOU whether you're the writer or the reader, and if that isn't the case something has gone horribly, horribly wrong.
*sigh* Strategy games are the worst represented in the good-story area, and C&C is the worst of them. Honestly, gameplay has always been fun in C&C games, but the stories are just.... just awful.
tl;dr Stories are love, stories are life, get storied.