I find this point about the Fitbit app very interesting. I myself own a Fitbit and the associated app, and this app allows you to monitor various things such as sleep patterns, physical activity, and even heart rate (if your model has that hardware). It gives the user some tools to better one’s lifestyle, similar to the app the OP posted about.
Where these two differ though, I believe lies in the application of the app. The OP’s app seems to be used solely as treatment almost for a disability whereas the Fitbit app is mostly for visualizing one’s activity. Additionally, it seems that the OP’s app communicates directly with an FDA-regulated device, which falls under the FDA’s definition of a mobile medical app. Contrarily, someone with insomnia may find use with the Fitbit’s sleep pattern recorder, but in the end all the Fitbit is doing is recording.