One of the authors here. Thanks for your comment! While a lot of this research is theoretical and does not have immediate use cases, we have tried to summarize some of them in the last paragraph of the paper (VII. Applications of Non-Euclidean Geometry). See page 26. We present some in Chemistry and Drug Development, Structural Biology and Protein Engineering, Computer Vision, Biomedical Imaging, Recommender Systems and Social Networks and Physics.
Thanks for the feedback! This model will evolve over time, we are planning on pushing a much higher resolution soon. Skill wise we will publish a paper in the next few months.