Video Quality and export is not great.

Your horizontal and vertical lines appear to be 1 pixel (one point) wide. Unless they are perfectly aligned with the pixel grid, they are going to soften because of antialiasing and the color is going to shift because MP4 video (world standard for sharing) compresses color in blocks of 4 pixels. It is insanely difficult to get accurate color on lines that are only 1 pixel thick. Lining up on the pixel grid is possible if you turn on Pixel Preview and Snap to Pixel in Illustrator and then carefully create the original artwork. You must check the work at 400% or better zoom with pixel preview turned on to make sure your edges line up with the pixel grid.

The same thing goes for your text. The horizontal and vertical edges should line up perfectly with the pixel grid. You have to check the AE comp at 400% or better Magnification Ratio and/or check the Illustrator file. It is also better for color compression if the horizontal and vertical edges of solid patches of color end up on odd numbers of pixel rows or columns. This is because of color compression.

A good workaround, that may work for your artwork is to make all of the thin lines 2 points in Illustrator and snap them to the pixel and check the artwork in Illustrator to make sure it doesn't fall apart when you zoom in with Pixel Preview turned on. You could also go the extra mile and make sure that the left and top edge of each horizontal and vertical line falls on the odd-numbered pixel. 

Your text layer can also be helped by adding a tiny bit of Bevil and Emboss layer styles or Bevil Alpha to put some detail on the edges. Just a tiny bit would help give some detail to the design that it just isn't going to have without some kind of edge enhancement. 

One more thing; I am fairly confident that you have Continuously Rasterize turned on and that you are not trying to customize the render settings without a very good understanding of video standards, compression standards, and streaming service recommendations for video. Just poking around in the render settings and sending YouTube, Vimeo, or anybody else that is streaming video a file that does not meet their recommended settings will always give you a lower quality product than you would get using their guidelines. The Adobe Media Encoder is up to date with its presets for all of the standard services so use them.