Since I started tabletop gaming mumblecough years ago, I've always found storytelling inspiration from the RPGs. From designing my character and developing his back story, to building a world and populating it with allies and adversaries, the games I've played have lived on in my imagination long after I've gotten up from the table and put the dice back in their bag. But it wasn't until recently that I heard Steve Jackson say "all games are role playing games, in their own way", and I realized that there's just as much inspiration to be found in tabletop boardgames as there is in tabletop RPGs.
I've been playing the hell out of the tabletop and iOS versions of the game Elder Sign. In addition to having a whole lot of fun trying (and frequently failing) to save the world from The Ancient Ones, it's inspired me to dive ever deeper into the world that HP Lovecraft created in the 1920s. I've been reading his stories, listening to their audio versions, and nudging my subconscious toward developing my own short story set in his world. Whenever my mind wanders these days, it veers dangerously close to the Mountains of Madness.
If you'd told me a few weeks ago that a boardgame that takes 45 minutes to play (and its iOS version that takes about 20 minutes to play) would capture my imagination and inspire me to try my hand at writing a Lovecraftian story, I would have thought you'd uncovered a Secret Man Was Not Meant To Know... but here we are.
This is one of the wonderful aspects of gaming, that I think gets overlooked: when we play games, we're using our imaginations to bring cardboard and plastic to life. If we're lucky, that spark can start a fire that burns long after the game has been put away.
By the way, if you're interested in Lovecraft, but don't know where to start, you may want to check out the incredible collection of Lovecraft's complete works that Cthulhuchick put together, and listen to the fantastic Stuff You Should Know episode about the Necronomicon. I can't recommend Neil Gaiman's I, Cthulhu enough. I also found this collection of Lovecraft audio works at archive.org that's pretty comprehensive and very well produced.