I actually used to do this a lot as well when I was younger, sometimes in a similar vein as pikapikapika in that I would attach my own characters and stories from my own mind to certain racing games;
Top Gear 2 for Super Nintendo comes to mind considering how bland the environments were (featureless landscapes with a "recognizable" background to indicate where you were in the world), and with the final track of the game being set in San Francisco (you can tell it's San Fran because the track is completely shrouded in fog!
) my plots for that game tended to be about finding one's way home from either a fun road trip or some kind of escape from captors/enemies. Similarly with
Stunt Race FX, the order and nature of each track lent itself to inspiring some journey plots in my head, especially with how much livelier and cartoonish that game's aesthetics were compared to the "realistic" TG2.
I think the games where I really took off with this were pro wrestling games. Besides trying to come up with my own angles and feuds with the existing real-life wreslters in each game, the bulk of my fun came from creating my own wrestlers, experimenting with different outfits and physical traits then defining their personalities with their movesets and taunts, while simply solidifying any back stories or connections with others in my mind. But I think I stopped with the whole angle/feud thing when I started playing
WWF No Mercy: when I first got the game I was excited by the idea of my own wrestlers automatically coming to the ring with actual belts you could win in story mode, but the infamous save file erasure bug prevented me from pursuing that endeavor and I settled for just seeing what kind of crazy characters I can create and just playing them in survival mode, which became the only way I could unlock stuff in the game.
I carried that latter habit with me in later WWE games, not bothering with any headcanons, simply just plopping crazy characters in the ring, before fading out of wrestling fandom altogether.
NBA games were similar with the advent of player creation and free trading, but the lack of more detailed attribute adjustments in early games, combined with my own idealism and pickiness in my desired basketball experience, meant not going as in-depth with the roleplaying and being more akin to my later WWE game habits, just plopping random created players onto the court and playing the same way over and over. But with later games being a bit more advanced I kind of went the opposite direction of my wrestling game experience:
NBA Street v3 not only had a really robust player creation system (tons of streetball moves, different ways to wear clothes, etc.) but also court customization as well, so I actually planned out some possible characters and team combos to play around with; unfortunately some changing priorities in real life at the time meant never getting around to following through with all that...but I still hope to revisit that game sometime. I know the recent
NBA 2K games have actual roleplaying features (My Player, etc.), so perhaps I'll give those a shot as well eventually.
Note the lack of actual RPGs in my gaming experience.
I'll touch up on more examples once I can better remember them.