I think i’m similar in that I really like this sort of thing but don’t often think about it. As others have stated, the game you’re playing can really lend itself to it. CK2 and XCOM are great examples. Battletech is another one in the XCOM vein.
For me any game where I have a squad of characters it can be fun to create stories out of the results of the gameplay. It’s not something I necessarily feel motivated to do for myself, but it can be fun to do on stream or through video.
I play a competitive turn-based football-like game called Blood Bowl in which you create a team of players based in the Warhammer universe. Each game you play, your players can gain experience and therefore new skills, but also gain permenant injuries or even die. You can knock players over that are standing as well as foul players on the ground. I generally like playing in leagues where I can keep playing my team for as long as they can hold together, and I like coming up with a theme for the team and player names.
One team I had was a mix of goblins and Skaven (Underworld) called Jazz Poison and had players named VX Gillespie and Ella Citronella. They had a particularly rough game against a Necromantic team that could turn an opponent’s player that they kill into a zombie for their team. I ended up making a video of a storyline that evolved as a result.
The fun part is that it’s a competitive environment so the story depended on my opponent’s input to make it so memorable. One of my favorite gaming moments of last year.