With hundreds of games, updates, dlc, mods, merchandice, videos and streams appearing each passing day gaming communities would get flooded by spam if no such rules would be in place. If you want to advertise on a commercial platform then you should do so through official channels.
Generally lemmy and reddit communities favor more organic content like for example solo game developer could ask for a feedback on piece of art of game mechanic they’ve implemented to their game in gamedev related communities. They could also participate to community events like screenshots saturday, share your progress friday or anything similar.
Now /r/gaming and /r/pcgaming are probably huge communities that are mostly about discussing gaming news, articles and just general topics around gaming. These communities are probably hard to moderate as is and allowing people to self promote there could lead to flood of indie or mobile game ads, streamers and youtubers trying to get more views for their vods or streams, etc which could really annoy the community.
If you want to make a fan game, make spiritual sequel instead.
Nintendo can’t do much about games that are very similar to Mario, Zelda or Pokemon for as long as they do not copy any assets, (some) names or levels from those games. Based on the videos the main character is unique but most if not all the other art assets are direct copies from the original game.