Sure. I don't know how familiar you are with TTRPGs, so I'll be exhaustive. While rules for TTRPGs can be greatly different when it comes to combat (if they have combat at all), they all implement some sort of skill checks for outside combat. Your character is good at some skills and bad at some others, which usually translates to having a modifier on the result of your dice, or rolling more or less dice, etc. In the normal flow of the game, the gamemaster describes a situation, the players tell what they want to do about it, and if what they ask to do is non trivial, the gamemaster asks them to roll for a skill check. If a player said they want to jump across a pit, the gamemaster may ask for an Acrobatics check, for example. The player rolls their dice, they succeed or fail based on the difficulty level the gamemaster decided, and the gamemaster describes the result.

When writing, I do basically the same thing. For each action my characters want to attempt (the key being to give them a deep personality through an elaborated backstory, so it is obvious what their personal reaction to an event will be and what decision they will make), I decide if it's non-trivial, assign a difficulty target, and roll to see if they manage to do it. Then I have my result, and I have to decide what happens. Did they succeed by much or barely? This immediately triggers the imagination about what may have gone so well or so bad. And this creates turns of events you wouldn't have thought about : if that character barely succeed jumping across that pit, it may anger that other character who is in love with them and terribly anxious. Which in turn may impact their next perception roll, as they are arguing while a lurking predator is getting closer. Depending on the theme, different skill lists and rulesets work best. I have three stories going on : high fantasy theme with Dungeons & Dragons, cyberpunk theme with Shadowrun, and Space Sci-Fi with Traveller. On top of the rules, they also provide tons of content to play with, like worlds to visit or equipment to try. That being said, I use them because I already have them, but any free ruleset found on the web would do, it doesn't matter that much, in the end (be it for writing or playing with friends, btw).

Since last year, I also discovered Mythic (the 2nd edition has been released sooner this year), which also helps randomizing the overarching story. I still prefer to decide on the main events, but it's great to add trivial details and side plots. It has a quite deep set of rules by itself, but the basic idea is to use an "oracle", which means asking a question, and roll dice to see if the answer to that question is "yes" or "no", with a modifier depending of how probable you think it is to get a "yes". Are there guards watching the side of the castle we're assaulting? Is the marchand trying to scam the characters? Does the king have a sense of humor? Those dice rolls can have quite an impact on the events. :) And when you don't know what to do next, Mythic offers keywords tables you can roll on to trigger your imagination. For example, let say we're in an antichamber, waiting for an audience with a queen. I roll dice twice on an event table, I get the keywords "support" and "distrust" (I've just rolled that). From that, I may decide an advisor of the queen is coming to see us and give us a hard time. Or, on the contrary, someone knows we're going to have an audience and ask us to have a word with the queen to advise her to be more cautious toward a third party. What is this third party? Let's roll again! "Excitedly" and "peaceful". Ok, that may be a neighbor country which has been very friendly, but people find they are meddling a bit too intensely in the affairs of the kingdom. And imagination build a world from there. :)

There are many single-player RPGs focused on writing and imagining. Often they're called "journaling RPGs".

Here are some examples! https://www.dicebreaker.com/categories/roleplaying-game/how-to/how-to-play-tabletop-rpgs-by-yourself

I've already heard mention of Thousand Year Old Vampire, never played it, though. There are a lot of things happening in the space of solo roleplaying which are boons for writing, but you will need several lifetimes to try them all. :) I stick to the three ones I use and already know well from tabletop gaming (dnd, shadowrun and traveller), and I don't want to start system hopping, because for me the focus is the story, not the rulesets, and it would get in the way. The only exception I made to that was to start using some parts of Mythic GM Emulator, because it can be used on top of the rulesets I use and it did indeed made my story way more interesting, especially when the pace is cooling down and you're not sure what to do next.