You're confusing two things:
The magnification of your composition view - ie: 'you're looking at your TV through a magnifying glass' : )
and
the scale of your layer.
Set your composition view back to 100%
Twirl down your layer and increase the scale property value. With continuously rasterize on the layer will stay sharp when scaled well above 100%. If continously rasterize is off it will become soft - just like scaling any standard pixel based image.
From your screenshot, I see that you have another serious problem. Your Illustrator files, if the layer is at 100% scale, contains lines that have a stroke of 1 point. That means the lines are 1 pixel wide. Here's the deal with video, if you have a line that is one pixel wide it either has to be perfectly lined up with the pixel grid and perfectly horizontal or vertical or it will be reinterpreted and change color and apparent thickness. A one-pixel wide white line shifted to exactly split the pixel grid will render as a 2 pixel wide light gray line. If you turn on Draft Mode the line will be 2 pixels wide and white, but if you animate the movement of the line and it does not move exactly an even number of pixels per frame, the size of the line will change as you move it and it will flicker and be hard to watch.
Basic rules, no strokes smaller than 2 points (2 pixels) and motion blur any movement that is not exactly a whole number of pixels per frame. Video does not contain or display vectors, it's pixels. Displays do not display vectors, they are pixels. The only reason that you can zoom in on an Illustrator file in Illustrator and not see pixelated results is that you are not zooming in on the actual pixels in the display. It would make no sense for a video editing or processing app to do the same kind of interpolation on the screen because, as I said before, video is pixels.
One more thing, a screenshot that does not show the modified properties of the layers giving you problems are almost useless in diagnosing problems. After you press UU to see the modified properties of a selected layer, if the solution is not obvious, just PrintScreen and Paste to the forum. It could not be easier. If you are on a Mac you'll have to use Shift+Ctrl/Cmnd + 3 and then drag it from the desktop.