All There in the Manual: The series has a couple of official documents for information about the characters and some of their interpretations; a Pokedex, a Fame Checker (Season 1, Season 2), a Lore Wiki, and a wealth of other sources of content that help explain some of the other lore for the characters and give off descriptions of their adventures.
Ascended Fanon: A collective, self-created instance, but this tends to be how the lore unfolds. Someone comes up with a good piece of art or an explanation for an indecipherable nickname, and if the fanbase likes it, the story rolls with it.
Big Name Fan: Several of the "mainstay" members of the mob have reached this status. There's Chauzu, who helps manage to the competitive balance of Arena, Addrash1, who is the current leader when it comes to having the highest Pokeyen in Arena, and Pioxys, who use to manage the Tumblr ask blog. Deku started out as this, but was eventually promoted when he came up with the system that allowed the mob to play 3DS and console games.
Fan Nickname: A lot of Pokemon have been given fan nicknames over the course of the playthroughs. Pokemon are often given unpronouncable names that are just random letters, so they are often given nicknames that are easier to remember and type. Many recieve nicknames that are based on they way their nonsensical nicknames might sound (like ZDNNNG the Skitty was named "Chairman Meow Zedong"), their powers or abilities (like Digrat, the Rattata who knew Dig and often used it at inopportune moments), or their supposed divine origin (such as Lord Helix, an Omanyte that came from the holy Helix fossil that Red looked at over and over again).
Follow the Leader: To the point when nearly two years later, on January 14, 2016, Twitch made a category called "Twitch Plays", where the requirement is the Twitch chat must have control on either a game or something else (but not people acting out feedback, as in the Old Spice Nature Man). Some examples, made before the category introduction, include:
Meme Acknowledgement: The app version of Twitch will occasionally recommend the user to consult Helix if the app fails to load properly.
Twitch Plays Pokemon as a whole has been indirectly acknowledged by The Pokemon Company International, who, as a part of the Milestone Celebration of the series as a whole, hosted a 24-hour marathon of Pokemon movies on Twitch named "Twitch Watches Pokemon".
There's a line from the French version of one of the later games, where an NPC says he got inspired to study Pokemon after observing a Helix Fossil for days.
The designer said that he might have turned the step count off in the Safari Zone if needed, but he wanted to see if it can be solved without that change first. Luckily, Democracy Mode helped make that possible.
They also stated that there would be no Emerald playthrough if Red was not defeated by day 20 of Crystal. Since Red was defeated less than a day after the announcement, we'll never have to worry about that. Hopefully.
Two of the games that were supposed to be played during the fifth season were Team Rocket Edition, a FireRed hack, and Metronome Sapphire, in which every move would've been replaced with Metronome. Due to the former being deemed to unstable by the development team to be played on stream, and the latter proving more difficult to set up than expected, they were replaced with Flora Sky and Fused Crystal instead.