If you mean the line doesn't have a single pixel width, this is what the website explains:
How is this 1D? The game is more than one pixel wide!
The game width can actually be adjusted, including to a width of one pixel. That's how I prefer to play, but other people had trouble seeing what was going on.
Regardless of how much you stretch it though, there is only one dimension of information, the horizontal smear is entirely redundant. Your computer's pixels have some amount of depth to them, but that doesn't mean the games you play on them have 3 dimensional viewports.
I had the same question and this answer didn't really do it for me.
Granted, I am bad at math/trigonometry/geometry etc., but in my understanding, 2D can only work from our perspective, because we're looking at it from a perfect angle.
Mario shouldn't see anything, because his viewing angle does not exist. Or is the rule about 2D that his perspective just has a width of at least more than nothing?
My lack of understanding can probably be explained with high-school material, but I can't imagine it myself.
Oh, you mean the physics of "seeing"? I thought the question was about why the vertical line is not 1-pixel wide.
As for "seeing": the real world is 3D. The physics of seeing work in 3D. I don't think there are true 1D or 2D objects in the universe, so we must use our imaginations when we say "Mario is seeing" in 1D or 2D.
We must, like others argued, imagine Mario possesses a way of sensing/seeing that works in 1D, something that doesn't exist in the real world.
PS: alternatively, the line is 2D in the sense that it's made of physical 3D pixels, and Mario can see those. But the line is also 1D in the sense its width offers no additional information because it's a single pixel wide; so it's physically 2D but "informationally" 1D.
His perspective is essentially the same as ours would be of four-dimensional space: The space can exist, we can move through it, but we can only ever see three dimensions of it at a time. It is the same for mario and the way that makes sense to you is as a line. Even if it is a line with no inherent width, that doesn't mean that Mario cannot see it.
Any point on the line can be described by a single coordinate, so the line is one-dimensional.
We could also describe all of them in terms of a two-dimensional plane [(0,0), (0,1), (0,2) etc.] but that would just be redundant. Just like representing the number line with a taller figure doesn't really make the abstract line any different:
So for a single-pixel wide view of SMB from first person perspective, we could consider it a degenerate case of a 2D view if we indexed them (0,1), (0,2), (0,3)... but that would be redundant as they're sensibly just 0, 1, 2...
Consider that any 2D image you see on your screen is just a single-pixel deep 3D image and a single-pixel 4D-protruding 4D image and so on.
Now I think the original question was about how Mario is capable of seeing at all something that is 1D, in the sense of "how are Mario's physical eyes able to perceive something that has only 1 dimension".
And he's right, Mario wouldn't be able to see a mathematical line (i.e. something truly 1D and infinitely thin), because there'd be nothing to reflect light for his eyes to perceive. I think the answer here is that Mario isn't an animal with animal eyes, and his fictional "vision" must work in different ways so that he can perceive purely 1D "mathematical" lines.