The title and abstract of the paper makes it seem like their approach can assure some form of absolute privacy. However, when you get down into the weeds of the article they really only have probabilistic guarantees. This seems like a problem because (1) most people will incorrectly assume the stronger form of privacy and (2) there is no objective way to determine the threshold required to be considered "private enough" for a given application. This is exactly the same as the issues I have with differential privacy.
In the end, I could see this being useful for protecting private corporate data where the concern is that the company does not want to lose the perceived value of their datasets just because they have released an external model using internal data. Theoretical guarantees that most data will be private should be good enough for this case. On the other hand, I would worry about using it on truly sensitive data (such as medical records) where even one compromised datum is of high concern.
It will be interesting to see how it plays out, but it's worth noting that there is a healthy amount of suspicion, some fear, and even a little bit of animosity toward google in the US health care industry. Opinions about surveillance and marketing (mis)uses aside, getting data can be a long and difficult process even for seasoned researchers in teaching hospitals. Personally, I don't fancy giving them my medical records any time soon.
In the end, I could see this being useful for protecting private corporate data where the concern is that the company does not want to lose the perceived value of their datasets just because they have released an external model using internal data. Theoretical guarantees that most data will be private should be good enough for this case. On the other hand, I would worry about using it on truly sensitive data (such as medical records) where even one compromised datum is of high concern.