I made Picturephone for two reasons. First, it serves as a kind of game for collecting data about how people make and describe sketches. It is a kind of "human computation" like Luis von Ahn's ESP Game for classifying images. Other researchers interested in sketching can use this data in many ways, like as input for training or testing machine learning algorithms. There's a more in-depth discussion in the paper.

I am personally more motivated by the second reason. I mostly made Picturephone as a way to have a fun sketching application available to lots of people. My research is focused on how people can interact with sketches, and what kinds of calligraphic interaction techniques work, and (most importantly) how those techniques work together. As of mid-February the version of Picturephone you use on the web doesn't demonstrate any of the fancy interaction techniques, but it will soon.