I think it depends on what you mean by good writing, seeing as it's you who needs to be satisfied. Simply using the five elements of fiction, we can try to determine what video games best fit your criteria.
The way that words are crafted for dialogue and descriptions, the way they are penned or acted on-screen, these fall under the element of style. If style is what you mean by good writing, then your best bet would probably be a Western-made video game; I'm assuming, of course, that you're going to be playing your video games in English.
Style is the primary concern of any writer undergoing formal training. Theme, setting, character, and plot - all of these can simply be given by another person to be used by the actual writer. At the end of the day, however, only the writer (and his editors) can determine the execution. This is why presentation, as opposed to substance, is given such heavy emphasis in writing courses. This is also why much of modern fiction can seem derivative or unoriginal - professional writers know they can simply steal each others' best ideas, and are resorting to outdoing each other using the same toolsets.
Regardless of whether you think this is good or bad, so long as your concern is with style, then it's better for you to start following professional Western writers rather than Japanese writers. Not only are English writers the more practised with using English, but the societal roots from which themes are drawn from will more likely be shared by them.
It's not to say that Japanese writers aren't concerned with style, or that they can't be familiar with Western nuances or traditions. It's just that Japanese writers must also become familiar with their own traditions and nuances when they undergo formal training, even the English majors (at least, this is the case for my country). While this may give a certain uniqueness to their literature, it is still very much an acquired taste. Expressing like for such taste is usually met with cries of weaboo.
As a commonly cited example for Japanese literary traditions and nuances, I will use those exact "world is ending/save the world" plotlines that you've just complained about.
In the Japanese society's consciousness, there still lies the losses of WW2. Air raids burning Tokyo to the ground to such an extent that the blown ashes of people were described as black snow; Mass suicides by civilians of Allied-occupied territories, having felt that they've failed in their sworn duty; The sheer shock of the atomic age ignited as both bombs fell; And at the end of it all, the emperor himself capitulated to save his people. For the Japanese of the time, the world had seemingly ended.
The Americas, for the most part, has not known such devastation. It did know fear during the Cold War, and its nose did get bloodied with things like Pearl Harbor and 9-11. However, it has never known what it's like to lose to the extent of hopelessness or loss of cultural identity. For the Japanese, on the other hand, a significant portion of their fiction is preoccupied with dealing with these issues - the Megami Tensei franchise and Yoko Taro games come to mind as video game examples.
While modern individuals do not have any actual faults or experiences with something that happened over 70 years ago, literature has this nasty habit of preserving these kinds of experiences. I'm not telling you to like these kinds of plotlines or anything, rather, I'm just explaining why it's so common in Japanese fiction.
Not only is there a cultural disconnect when it comes to themes and traditions, but Japanese writers must also contend with the translation process when presenting their style in English. A good Japanese writer, with a nuanced Kanji vocabulary, whose game receives an ill-fitting translator will still come off as a bad writer.
Going back to video games, many of the goto answers have been said. I'll just second those who are suggesting staple WRPGs (FO1/2, PS:T, Arcanum, etc.) if you haven't played them. I originally planned to also talk about character as well in helping determine a good game for OP, but holy shit this post is really long now.
Also, while I talked about style in the view of literature, gameplay and design would also fall under criteria of style if videogames are viewed as works of fiction. This would be a means of circumventing at least a little of the problems caused by nuances between languages - where appreiciation is tied to universally experienced phenomena such as with visual arts or musical arts. Games where the writing is tied-in with the gameplay, are able to communicate the writing in a way that is distinct from the actual words used in dialogue or descriptions. Of course, I think that's a discussion for another time altogether.
Vanillaware isn't really known for its writing.