Do we use 3x3 matrices in computer graphics?
That quote is a very strange way to phrase things. We definitely use 3x3 matrices in computer graphics. They tend to be most useful for doing affine transformations of 2D objects. It allows you to have scale, rotation, shearing, and translation (in 2D), but not perspective transformations. I believe that's what the quote is trying to say.

To get a perspective projection of a 3D scene onto a 2D plane (such as your computer screen), at some point you will need to divide the x and y components of each point in your geometry by some factor that foreshortens lines in the z dimension. That's the divide that they are referring to. See this article for more details. In it, they describe:


  The simplest perspective projection uses the origin as the center of projection, and z = 1 as the image plane. The functional form of this transformation is then x' = x / z; y' = y / z.