Why use images of reads when you already have the reads data?
Neural networks take one or multiple N-dimension arrays (n-d arrays) as input; they can't take arbitrary forms of data. To feed reads and their alignment into the network, you have to encode them as n-d arrays. If you ignore "colors" for now, a straightforward choice is a (windowLength, readDepth) 2D-array as you see in an alignment browser – it is an image. The "colors" of this image are often called "channels" or "features" in deep learning (DL). They represent base types and base quality in deepVariant. In the end, you get a (windowLength, readDepth, nFeatures) 3D array as input. This is the most natural encoding to DL researchers.
Why chose CNN for a variant caller
That is because CNN has been repeatedly proved to be the best architecture for such (height, width, nChannels) 3D arrays as input. Read alignments are exactly that.
On a historical note, deepVariant was first built on top of google's now-deprecated DisBelief framework that only takes RGB images as input. They had to squeeze all types of information into three color channels. Now with TensorFlow, an image can have an arbitrary number of color channels. This simplifies implementation and improves accuracy. In addition to this image, deepVariant also takes other information as input.