First, in address to, everyone who's responded, I think Bright Sun Studios has a bit more merit to their argument than you're letting on. If you've played Blooming Love, BSS's game, then you know that they know how to craft a modern story that is completely character driven, and that doesn't do much to build the world beyond character conversations. For the most part it relies on it's two main characters to bring life to the world and it's story. The story isn't less compelling because we don't know what's going on around them, because it's simple to build that world for ourselves, as we all live in a modern world with the same rules and structures as theirs has.
Fantasy and Sci-Fi, though not brought up, have a need to explain more. As
@Oiz pointed out, you don't have to build the entire kingdom, just the relevant parts, but you do have to define the relationship of this small village in the woods to it's neighbours and the world it interacts with. This is because we don't have that information, and it is going to be relevant to the plot. The artist InCase has an ongoing comic about a halfling girl named Alfie. In the beginning we are introduced to a new world and characters, the village they live in seems to be a halfling community, they are currently trading with a travelling band led by an extremely wealthy elf, and his human guardsman are part and parcel to the story. We know that Alfie dreams of adventure and that these humans are alien to her. We know a ton about the world, and we learn all that in the first idk, chapter? It would be about the length of a single game release... maybe two to get the information about the elf and that the guardsman Alfie speaks to is part of his caravan. These little details can be completely ignored in a modern story, because in a modern story we know how humans interact with their world.
That out of the way, I'd like to address some of your concerns Bright Sun Studios.
I would generally have to agree. Most of the ones I've played tend to add fantasy willy nilly. They'll often attach a simple hand waving explanation as to why you're so weak now and what to do to become stronger, but that's about it. But then you've got a game like Coceter Chronicles which goes to great lengths to make a world that feels lived in. There are lore objects around the various maps that introduce you to a vibrant and important history. Your character's future is hinted at from the beginning with vague secrets and disobeyed laws. Laws? That's right, you know that the law has been broken because you were told there was a law to begin with. The game is constantly dumping information on you... even now, fleshing out more and more.
Long Live the Princess isn't as good at fleshing out it's world, but it's also working with a more secretive plot, it gives us more when we uncover it. As we do though the intrigue thickens and I wonder more and more about it. Another good example would be Kingdom of Deception, in which the dynamics of the world, the history of the war between humans and orcs, the politics of the orcs, the skills available to Sabia, all of it, are pretty well explained. But then there are others which instead of explaining where we are, try to just tell us a character driven story with no detail about the world or why it is the way it is or who is who and why. As I said in my opening arguments, you can do that in a contemporary setting. You can't do that in a world with different rules and settings.
If you want to borrow from a source to make your story I'd suggest D&D. While each of those you've listed have rich and engaging characters and worlds, they've all built on what came before, and what came before was LotR. The thing with D&D that makes me suggest building from it rather than building from LotR, is that LotR has a defined and bookended story. D&D which also borrowed from LotR, created a world that is meant for people to simply pick it up and create their own story.
What's best about it though, is it's also possible to create your own completely unique thing, simply using it as a building block. You can use it's magic systems and character classes on top of your own unique lore. You want a race of half demon creatures you can design them based on the Tieflings, you want a holy warrior? Look no further than the Paladin. You need inspiration to create a pantheon of gods? Hello we have several gods to look to. What you do is pick and choose the things you like, the aspects and behaviours, and add your own names and a unique spin on their relevance.
The best part is, you don't have to take it all, just he pieces you want or need to create the world. Dragon Age and The Witcher have absolutely done this. Bioware made Forgotten Realms games before making Dragon Age, and Forgotten Realms is just D&D's licensed story stuff. Elder Scrolls I'd say has taken more from D&D than others. Specifically because of their different races among elves, and the fact that Orcs are simply a race of beings, not a corrupted version of another species, like they are in LotR.
Then you've got Sanderson, and Sanderson is the outlier, he's the one who looked at what came before and said, I wanna try something different. Where Gandalf's magic was a deus ex machina when the plot needed it, his magic would define his character's actions and interactions with the world. Where morality stood squarely on the side of the fellowship, his villains are more grey. Where LotR used elves and dwarves, he decided to create his own races. If you wanna go the Sanderson route more power to you, but that means a lot more legwork on your part in introducing us to the world.