Well, it could be about Naruto having the Rinnegan and also having some sort of gamer - like abilities. Maybe he uses his new powers in the context of the game - like elements in the Naruto world. For example, he might level up his Rinnegan skills or face challenges as if they were game quests.
The main character is Naruto for sure. But in addition to his regular comrades, there could be new characters introduced specifically related to the gamer aspect. For example, there might be a character who acts as a sort of 'game master' in the Naruto world, guiding Naruto in understanding and using his Rinnegan in a game - context. And his friends would still be important, with Sakura perhaps being the one to heal him during his more dangerous 'game - like' battles with the Rinnegan powers, and Kakashi could be a mentor figure in how to combine the Rinnegan and gamer strategies.
The Rinnegan OC can stand out by having a moral code that is different from the typical characters in the gamer fanfiction. For instance, they might use their powers not just for victory but also to protect the virtual world's inhabitants in a more selfless way, which would make them a more complex and interesting character.
One idea could be an OC with the Rinnegan who has the power to manipulate game glitches in the virtual world of the fanfiction. They could use it to their advantage, like teleporting within the game or accessing hidden areas.
One implication is that he becomes much more powerful. The Rinnegan gives him access to powerful abilities like the Six Paths techniques, which would change the power dynamics in battles in the fanfiction. He could now face stronger enemies more easily.
In Naruto fanfiction, the Rinnegan in Naruto is often portrayed in really cool and powerful ways. Some fanfics might give Naruto the ability to use all the Rinnegan powers to their fullest extent right away, like being able to effortlessly summon the Gedo Statue or use the Deva Path powers without any drawbacks. It's a way for writers to explore new storylines and make Naruto even more of a badass than he already was in the original series.
Another possibility is that it's a result of some strange chakra experiment gone wrong (or right). Scientists in the Naruto universe are always dabbling in chakra research. Maybe an experiment meant to enhance her natural abilities instead gives her the Rinnegan, and she then has to learn to control it quickly to avoid being consumed by its power.
If Naruto got the Rinnegan, he might become more cautious. The power of the Rinnegan is so great that he would realize he needs to be more careful with it. He wouldn't be as brash as before.
Well, when it comes to Naruto time travel and Rinnegan in fanfics, it's often about exploring new storylines. Maybe Naruto himself gets the Rinnegan and travels back in time to train his younger self. This would make him a much more powerful ninja at an earlier stage and could completely change the power balance in the Hidden Leaf Village and among the other ninja villages as well.
There's a fanfic where the female Naruto gets the Rinnegan and teams up with some unexpected allies. This fanfiction focuses on her journey to understand the true nature of the Rinnegan and how it can be used to bring peace to the ninja world. It's a great read as it shows her growth from a young kunoichi to a powerful force with the Rinnegan.