There are more ways to tell stories in RPGs then just in the direct path of an adventure. Like with videogames, almost everything players interact with can help inform them to more about the world, the NPCs, and even yes the main story or stories you're trying to tell. Today I want to touch briefly on ways to get these small bits of stories across.
Everything Has A Story
Humans are natural story tellers, and the world we grow up in is one full of stories. As such it makes sense to think that everything we interact with has a story. Some of those stories are boring. The story of the monitor I'm currently using while typing this isn't particularly eventful or intriguing, but it is one of constant use that further tells the story of me - a person who mostly sticks to themselves and is on the computer more than is good for them. Keep this in mind - everything has a story, not the bit about me - when designing things for your game. You don't need to go into pages and pages of details, but what is the core story of the thing and how can you get it across?
Stories Enrich The World
The second thing to keep in mind is that stories enrich the world. With everything having a story, if you can convey that in your game, it will enrich and deepen the world. When the PCs come a cross mini-stories in progress, or see that places have stories of their own, it gives a sense of history and action that happens when the PCs aren't around to see it, and that in turn helps the world feel real.
Story in Description
One place you can easily drop in bits of story is in the descriptions you use when talking about places, people, and things. A dragon with missing scales and battle damage indicates it's been in a few fights before. A starship with pristine lines, polished hull, and not a mark on it tells the story of it being a new ship. You can use this to fulfill the old writer adage of showing not telling, and it can work well. In Lost Mine of Phandelver, the town of Phandelver tells the story of being built on the ruins of a previous settlement with the bits of stone walls that surround various property lines.
Story in NPCs
NPCs can literally tell stories, but they can also live stories. Everything about how an NPC acts is part of the story of who they are. How the NPC dresses - i.e. your description of them - also tells a story of the NPC. You can convey almost every aspect of how an NPC will act or where they came from with how they're dressed, how they carry themselves, how they present themselves to others. You can intertwine their personal story - if they have one you plan on bringing into the game - with other parts of the world and thus tell more about your world through them.
Story in Items
Magic swords and named weapons have stories. But so to do all the ones without names or legendary qualities. Their stories, like my monitor, are not as interesting but they can reveal more about worlds, people, cultures, and so on. There's a reason the Katana is no prominent in so many stories, and it is because it links the story of people wielding it back to the general fascination western culture has with Japan, the Samurai, and the romanticized stories we tell about both. By the same token, Roman Legionaire garb will convey a whole lot about an NPC and their home culture just because of how deep it goes in our own understanding of the world and Rome.
You can use this in other ways too. A group of people using bone weapons speaks to more primitive cultures, but adding refinement to that concept can also get you thinks like the Fremen Kriss Knife which has a story not in the particular weapon, but in what the weapon is and means.
Weaving these all together gives you a deeper tale. How in depth you go is up to you, but going more and less deep depending on where and when can let you throttle your investment to impact while continuing to give glimpses into a deeper, more real world...even if you don't have it all sorted out already.