Well, no story is going to entertain everyone, so you might want to check if others consider it boring or just you. Some genres of game are heavily story-based (RPGs, some adventure games) while some have basically no story (most arcade games), and there are in-between games which have only a few paragraphs of story spread out over the whole game (RTS games, CCGs/TCGs, some platformers and sidescrollers, some FPS games). If you are a gamer who prefers games that don't have much story, but you end up with a job making an RPG, you are probably going to find the story boring no matter how good or bad it actually is.

On the other hand, if you enjoy reading and playing games with a lot of story, and further if you like the particular genre of story in question (fantasy? sci-fi? horror? drama? comedy? tragedy? romance?) then you might actually be a good judge of whether a particular story is boring. The question of "what makes a story exciting?" is about half personal taste and half serious writing technique based on psychology. I'm not sure I could really explain to someone who didn't have a background in writing, but suspense, pacing, and emotion are the main ingredients, and with games it's particularly important how you combine the story with the other game elements like combat, cutscenes if you have them, art style, and sound design.

As far as "how stories are written?", that could be 2 different questions - writing process and techniques, or story structure and mechanics.

If you want to talk about writing process, a writer has different options for where to start: a character idea, an idea for a relationship between two characters, an idea for a unique world, an idea for a particular plot event, an urge to write about a particular theme, an interest in making the audience experience a certain emotional atmosphere, or the question of what type of plot and character would be best for exploring a particular gameplay. These options are called the circle of story design elements; they are like a circle because no matter which one you start at you have to work your way around to all of them to create the first draft of a story concept, then you have to go around the circle again to flesh out and add detail, and then you can repeat that to fill in holes and add more detail. An iterative design process, basically. Ideally story design and gameplay design should take place in parallel - first you decide on a rough concept for both, then you refine both, etc. Sometimes writers are stuck in the bad position where a game has already been 3/4 completed with no story and the writer is asked to paint a story on top, and to do that cheaply by requesting a minimum amount of changes and resources to make the game support the story. This unfortunate situation is especially likely to produce boring stories because many interesting ideas will be discarded due to the restrictions of the design.

Structurally, a game story concept will start out as a concept or pitch, which is basically a paragraph or two briefly describing the main character, the world, and the plot. This is then developed into a synopsis, which is 5 or more paragraphs thoroughly describing the main character, the world, and the plot; usually the plot will be broken up into acts, chapters, or locations where each part happens. For a linear game this is pretty straight-forward, but for an interactive or open-world game a flow chart, map of the game, or several parallel timelines with story chunks placed along them may be needed to organize the information. This is then developed into a script, which is comparable to the script for a manga/comic or an animated movie. The script includes not only text that will appear in written form in the game, but narration and dialogue, which may then need to be recorded by voice actors. In some cases the script may include the text for sign posts, posters, magic circles, or other graphics that will need to appear in the game. It may be helpful to assign an ID# to every piece of text or spoken dialogue intended to go into the game; this allows you to script stuff like: If the player talks to NPC Joe, NPC Joe says #J309, unless event #Dungeon03Clear has already happen, then Joe says #J415.

Your average game still doesn't have good story, so if you're asking how the average game studio handles story I think you're trying to imitate the wrong people. That's like going to a crack house to ask advice how to handle addiction.

I think the question you should be asking is how SHOULD stories for games be written.

You may take a look at coursera's course for script writing.

They focus on such properties of a script like 'compelling' and 'intruiguing'. There's a few of theory tho.

sunandshadow is right, you just write things. You start with a pitch or even with so-called mini-bible where main and minor characters are listed, and then you outline a few episodes / moments / quests, and so on.