For anyone non-familiar with the nomenclature. TAS stands for "Tool-ASsisted" run, which means running the game on a special emulator and playing it with additional help of features like save-states, slowing the time down or even inserting input frame-by-frame. The emulator keeps track of controller input for every frame and then is able to "playback" it so it appears as it would be normally played by a super-skilled player.
While some consider TAS runs as "cheated", they have their own niché, because usually they are pretty entertaining, showing what can be achieved in the game that's otherwise not possible in real-time runs, showcasing game glitches, and so on.
The about page of TASVideos.org now defines the term as "Tool-Assisted Superplays".
I'm pretty sure that is a re-definition of an acronym that began life as "Tool-Assisted Speedrun". It's worth noting that the video you linked to talks a lot about "saving frames" in its description - not something anyone would care about if speed wasn't still a thing on their mind.
The actual live speedrun/TAS communities seem to get along fine. TASbot has been well-received at Awesome Games Done Quick, for instance. I think it's generally acknowledged that live speedrunning is meant to push human skills to the limit, while TAS is meant to push the game to the limit, and that these are complementary goals (and that both require a great deal of cleverness).
That doesn't change how every YouTube video of a TAS has comments along the lines of "this is dumb, ur cheating lol". But YouTube comments are always bad.
Before that was the Ocarina Of Time wrongwarp trick [1] that became so ubiquitous in real-time runs that real-time and TAS are going head-to-head nowadays (The TAS times are actually slightly slower, due to including the title screen/outro sequence in their measurements).
https://www.youtube.com/watch?v=LoThCyif9Oc
There are a few similar runs of other game sets on TASVideos:
http://tasvideos.org/Movies-C2020Y.html