As a few other other have pointed out, the data from this game is open-source and accessible in number of ways [1].
For an introductory exercise to deep learning for image classification, it's a great alternative (or follow-up) to the classic MNIST dataset [2], which serves as a common "Hello, world" for image-based ML.
We trained and deployed such a model for a demo of our mobile ML tool [3][4]. Feel free to ping me if you're interested, would love to chat.
[1] https://github.com/googlecreativelab/quickdraw-dataset#get-t...
[2] https://codelabs.developers.google.com/codelabs/cloud-tensor...