Speedrunning is a spectator sport, so spectators ultimately determine which categories are the prestigious ones.
TASes break every rule and are pretty cool.
There's still rules in TASing, just a different set of rules! Specifically, you have to submit a file containing a sequence of controller inputs that completes the game when played back in an accurate emulator (or a replay device connected to the controller port of an original console running the original game).
I co-authored the current fastest TAS of Super Metroid: https://youtu.be/m-Gt57ur7OA?t=2m30s We completed the game in under 2 minutes of gameplay by exploiting a race condition in the game's sprite animation system to start an exploit chain leading to full arbitrary code execution (full writeup: https://tasvideos.org/8214S ).
We used all kinds of tooling to create the run: a recording emulator with savestates, slowdown, and frame-by-frame input editing, scripting tools, debuggers, disassemblers, and memory viewers. We used memory editing tools during development to test different scenarios without having to set them up in-game first, but the actual run you submitted is completely "pure"; just an input file that beats the original, unmodified game.
And just like real-time speedruns, TASes are split into categories too. Here's the world record TAS with major glitches disallowed, by Sniq: https://youtu.be/Rr9gdQ-VkO4 Whereas our ACE TAS is more like a CTF challenge than anything else, Sniq's run is a masterpiece of gameplay that shows how far the game can be pushed beyond the current human limits. But again, it's still a true run of the game; the only difference is that you submit an input file instead of a realtime performance of the run.
Enter TASBot: https://www.youtube.com/watch?v=rha61Y3_Voc
It's a really cool project. In case "just" running a TAS on a real console through some wired up controller... Nintendo DS is also supported: https://www.youtube.com/watch?v=MHQCJX0RzS8
It's such a funny and rewarding escalation of the really impressive world of TAS.
This process had already been going on before, but you have this progressive sequence of the speedrun getting harder to play and harder to watch. You see some spliting out to restricted categories but even those aren't all that popular, but also something else that's recently become really common particularly in the communities for these games that have been optimized to death: randomizers. Shuffle around the positions of the necessary items, or the map itself, and you have something that's fresh for viewers and people who've played the game forever, an extra aspect of chance, usefulness of skills and familiarity with parts of the game that wouldn't otherwise be relevant... but it does split the community even more.
(The debate was sparked by a runner proving that the trick was humanly possible, raising the spectre of someone actually pulling it off in a world record run, which would force all subsequent world record would-bes to replicate a trick that would kill 99.99% of runs, execution of which depending on the vagaries of how different controllers poll inputs in addition to nearly inhuman levels of sustained, frame-perfect inputs).
Fairness: generally speaking the competition wants to be fair. Part of this is just having a consistent set of enforced rules, but it also comes down to decisions about timing and allowing or disallowing certain tricks: if how fast part of a game is depends on how fast your hardware is, for example (whether by a trick working or simply lag), then most communities will try to eliminate this effect by banning hardware-dependent tricks or adjusting timing rules to remove loading times.
Competition: At the end of the day speedrunning is a competition around a game, so there's a general resistance to modifying the game itself, or e.g. use of external tools to assist the player beyond what was intended by the developer. But that will sometimes be compromised if there's some aspect of the game which badly affects other goals.
Fun: At the end of the day, speedruns are something that should be fun and rewarding to play and watch. So if the optimal run of a game becomes unfun to play or watch, then generally something will be done about it, whether by banning the trick which is unfun or by allowing something which alleviates the pain point (sometimes this even verges into health concerns: some pokemon games, for example, have very long runs with a huge amount of button-mashing to get through dialogue quickly, and RSI is a very real concern which means that turbo controllers which automate that are sometimes allowed). This can go as far as patching the game to remove particularly unfun or RNG-heavy parts, though it's rare.
And of course you can have different categories which will focus on different aspects of this, especially as different runners and watchers will have different ideas on what is fun: apart from what counts as 'beating the game' (any%, 100%, 'true ending', whatever), there's different levels of what other compromises are allowed. And it can get pretty contentious: from hardcore 'play the game as intended' purists to arbitrary-code-execution TASers, everyone has a different idea about what they enjoy in the competition, and different games can have strengths in each area of focus.
There are run “categories” for any given game. Super Metroid’s arguably most prestigious category used to be called “Any%”, referring to the required item collection percentage as distinct from 100% or Low%, and now it’s called “Any%, No Major Glitches” because someone discovered that you can go out of bounds with the X-Ray Scope and a door. It specifies “major” glitches because the run otherwise makes heavy use of (among others) a “minor” glitch called Mock Ball, which lets you move in morph ball form at regular form running speed. Ultimately, the community has to agree on what is major and what is minor but it’s usually moot until a new exploit is discovered.
It is interesting and it makes a whole lot of sense once you look at it from this angle. The categories actually have pretty rigorously defined rules precisely because there is so much competition involved.