AnimeMusicVideos.org has its own definition of what is considered anime for database purposes... this definition doesn't exactly match others. For example: video game cutscenes are considered anime, but I doubt they would be considered such by other definitions, especially the ones rendered in real time by the cpu and not just actually stored as videos.
We recently had a discussion on how to update our definition of anime
here, but American animation, in which "Avatar: The Last Air Bender" falls right into, would not fit in. This is because we're starting out with the English meaning of the word anime, and trying to give it more clarity since, as it generally stands, it is a rather blurry definition. One of the things suggested was to consider anime as "Japanese looking animation." The main issue with that definition is that it doesn't really make things any clearer since Japanese animation itself has quite a widespread amount of different styles and so on.
Let me give a good example: would you consider "The Powerpuff Girls" as anime-looking? Most people would reply no to that, seeing how the style is so far from what is usually considered "anime." However, the recent "Panty & Stocking with Garterbelt" anime by GAINAX has a visual style very closely reminiscent that of "The Powerpuff Girls," so clearly, if we went by the "Japanese looking animation" definition, people would argue that "The Powerpuff Girls" should be considered anime and they would have the right to. By using similar arguments one would be able to get animation such as "South Park" or "Happy Tree Friends" considered as anime, but we doubt they would really fit in.
So, as you might now realize, the key point here is keeping the rules as clear as possible. Generic definitions don't help, and while we won't ever be able to fully remove a "grey area" that will require a case by case evaluation, removing possible doubts and misunderstandings in the definition is something to be sought. Thus, when some kind of animation falls into a grey zone, it is safer to cut it out or reserve the right to decide case by case, rather than change the definition to fit it in with the risk of blanket-allowing anything and everything through some astute reasonings.
That said, keep in mind that you are not prohibited to enter and upload music videos using Avatar, just as long as the footage used is actually mainly anime; what I mean is, you're allowed to mix in kinds of footage that are not considered anime (such as American animation or Live Action) in your music videos as long as the majority of the video still is made up of anime.
Hope this helps...