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I think it is reasonable to consider Twitch Plays Pokémon a video game with non-obvious game mechanics that deserve an explanation. While I would rather have us cover the event through questions about Pokémon Red itself (say, "What is the optimal route through the Safari Zone?"), I think those questions are on-topic, relevant and timely.

Original image courtesy of FEichinger in this very same question.
The argument made by FEIchinger is that, since the question is about what happens on the green side, and the game is on the red side, the question is off-topic. Nothing could be further from the truth. Allow me to abstract the situation:

On the left side, we have the player-side part of the program. You have a window in which you can issue commands. The commands go through the network through a set of so-called RPCs (remote procedure calls; the name is not important) and the game server reads your commands and acts on it. The game server then sends you the answer back with the updated state of the game.
Does it sound novel or extraordinary? It shouldn't. Here's another example of this configuration:

I'm going to pick World of Warcraft here, but this is the description of almost every multiplayer game ever written. Every game that has a server is comparable to Twitch Plays Pokemon.
- When I play World of Warcarft, I open the World of Warcraft application (green) and give commands at it (blue arrow rightwards). These commands are sent (rightwards arrow) to Blizzard's World of Warcraft server (red box), which gets my input and processes it, resulting in the casting of spells. The server gets back to the client (leftwards arrow) and tells the client that yes, you had enough mana, you were still alive, you did have access to the spell, so the spell was cast.
- When I play Twitch Plays Pokèmon, I open the Twitch application (green) and give commands at it (blue arrow leftwards). These commands are sent (rightwards arrow) to the Twitch Plays Pokemon server (red box), which gets my input and processes it, resulting in the pressing of a button. The server gets back to the client (leftwards arrow) and tells the client that yes, your button of choice has been pressed.
Saying that questions about the left side of TPP are off-topic is saying that we do not want questions about the World of Warcraft application. All troubleshooting questions are now off-topic. All questions about configuration are now off-topic. All questions about the interface are now off-topic. All questions about chat are now off-topic.
Ironically, FEIchinger got the situation entirely wrong. He argues that the only part of the setup that's our concern is the red one. Nothing could be further from truth.
What happens on the red side is actually off-topic. We don't want questions on how to be Blizzard and operate and maintain the World of Warcraft servers. Similarly, questions about Twitch Plays Pokemon should not ask about Pokemon Red, or the IRC bot that feeds it input. Questions about Pokemon Red should be tagged Pokemon Red.
We are very much about the green box. Making it work, understanding its user interface, its commands, making it do our willing: this is very much what Arqade is about.
This is clearly and patently absurd, and not how we have operated this website for the last 3½ years. We should not panic over one borderline question and singlehandedly destroy the site in the process.
But badp, I hear you cry. This can't be right! Pokemon Red is a game! Twitch chat isn't! Have you gone insane? No. No I have not. See, there is a little thing out there called cheats. When you have a server-client program where some of the clients may be compromised (say, gold farmers), your main recourse is that of using a "thin client." What this means is that all the client knows is how to render the game state and how to send inputs. The game itself - the game logic, the game state, who is where, who is doing what to whom, what map they're in, everything - is right on the server.
Even in World of Warcraft, the actual game code is on the red side. All the green side does is send commands and get frames back. And yet it's the precious, precious green side the part that we commonly call "the game." It's the part we install, it's the part we maintain, it's part we mod with texture packs and shaders and HUDs and polygons and anti-aliasing and all the delicious client parts that are so dear to us and are, ultimately, what this website is about.
This might be far and abstract because the World of Warcraft servers are only in Blizzard's hands, but since this is almost every single multiplayer game ever made, Minecraft comes to the rescue. Even when you play in single player mode, Minecraft has a thin client that connects to the server side with all the game logic. The client only knows how to render the world as downloaded from the server.
All of this is precisely, identically, indistinguishably, exactly the same deal with Minecraft, and World of Warcraft, and Team Fortress 2, and Starcraft, and Quake — and, likewise, Twitch Plays Pokemon.
(Exceptions are games that operate in peer-to-peer. I'm not aware of any.)
Visual thinkers may find my argument in this diagram:

What I need you to understand is that if we decide that TPP is not a game, we must do it sensibly, on grounds that make sense when looking at the big picture, without necessarily take half of our topic with it. So far, in order to outlaw Twitch Plays Pokemon, we have tried in turn to outlaw every game with a menu ever, every game with a community ever, every videogame with luck elements in it ever, every hidden object game ever and now every multiplayer game ever. All for one question about start9
.
If TPP is truly different from EvE online and its bretheren and we want to give a reason as to the difference, we must be more careful. This website is 3½ years old. This question is not going to open the floodgates for thousands over thousands of terrible questions, and even if it does we should let the floodgate open anyway to have some actual data and discriminate the good from the bad. We can't do that on one question and one game and the super-generic tone of this question is not helping.
This should make you pause and think on what actually we are trying to achieve. Is it worth to destroy this website over one question?