I hope you like people being picky. If you don't, ignore this post.
A few small nitpicks. You seem to have the basic gist of the community down pretty well, but some of the specifics are a bit off.
The main goal of the site is to have entertaining runs. You kind of touch on that a bit, but I think it could be pushed a little more. Tool assisted runs are meant to entertain and surprise the viewer. It's the philosophy which causes the speed vs. entertainment debate that happens every once in a while.
Also, see this category
Alternate goals are usually chosen with this idea in mind. When an alternate goal is picked, it's usually because it would be slower, but the goal has entertainment value in itself. The 2 player run of Chip and Dale is faster and thus not a good example. A better one might be Nightmare on Elm Street, where the run is slower, but more players is more entertaining.
A list of runs where using more players is actually slower, but the choice was made for entertainment purposes (There may be more).
You used Gradius as an example of a no damage run. That's actually not a good example because the nature of the game actually forces you to take no damage (otherwise you die). You should look for a movie where taking damage saves time, but the author decided not to do it (those are becoming increasingly rare).
For different characters, I would have used
[976] NES Super Mario Bros. 2 "warps, princess only" by adelikat in 08:29.57 as an example. Princess Peach is not the fastest character, but she changes the gameplay significantly, which is why we made a separate category for her.
Speaking of Street Fighter II, you say that those runs are as fast as possible. They're not, and intentionally so. A fastest possible would be too repetitive.
One category I love (and it can replace one of your other categories) is glitch avoidance runs. If people decide a glitch makes a run too boring, repetitive, or breaks the game too much, runners make another movie that doesn't use that glitch. These often lead to much more interesting runs than fastest possible.
Here's a list. (This really needs to be kept track of better) There are others where glitches were found, but the unglitched run is still available on the site. I didn't include those because they were cases where the original author was unaware of said glitches, but they also might count as demonstrations of the concept.
The presentation is well put together and would probably turn many people on to the idea of tool assisted speedrunning. I thought the videos were well integrated and it covered many good points. It's kind of sad that the video of Rayas TASing seemed to stop halfway through, though.
