I would just like to start by saying, I am very glad that we can exchange our thoughts and opinions like mature individuals here, even though we may disagree.
I know some forums would have already degenerated into a massive flamewar over my comments.
That being said, onward.

Allow me to address your first point concerning Eboy's art.
It is difficult for me to imagine their work as anything other than art, I mean their works are color and lines in an aesthetically pleasing fashion.
I think this fits the basic premise of a two dimensional work of art.
(I would really like to hear what you think makes their works not art, so I could elaborate in a more specified manner.)

Personally I carry an extremely broad definition of the word art, I include everything from film, music, sculpture, paintings, graffiti, sidewalk chalk drawings done by a three year old on the pavement, screen printing on t-shirts, idle doodles in the margins of notes, album covers. I could go on and on, but I think you get the point.

When I said design was art applied to the practical world, I mean, objects by design are utilitarian, take shoes for example, by design they are only a means to shelter our feet from harm, but the through the application of art we make them aesthetically pleasing.
The shoes aren't like a traditional piece of art, that hangs on a wall, but they still display the aesthetic principles we, as artists, use for our guidelines.

Your third point of discussion really brings us into muddy waters.
I understand that this is a forum reserved for pixel artists, I don't think it would be appropriate for an artist, such as a watercolor painter, to come here and ask for critique.
However, let me pose this question to you.
What if the watercolor artist had painted a mural of a building on a hilltop, then scanned the image and "pixelled" the building.
Leaving a final image of watercolor style hill and a pixel art building.
Can he still come here for critique on the pixel portion of his painting? Or must we completely disregard his artwork because it follows some but not all of the requirements here?

One additional question for you, Anarkhya, do you think architects are artists?

(edit: there was a confusing grammatical error.)