There are several problems with lay individuals using this app. As with most auto-refractors it presumably does a fairly good job in determining an individual's prescription (research is ongoing), but it is probably not useful for all populations (children and patients with special needs may be an issue). Also, it does not take into consideration the special needs and preferences of the patient (work, sports, distance needs, near needs, etc).
The other issue is one of legality. Currently individuals must have a prescription determined by and written by a doctor. Otherwise that prescription cannot be used.
Remember that an eye examination not only includes an individualized prescription as determined by your doctor, but also an assessment of eye health, binocularity and more. A refraction alone is seldom enough to meet most patients' needs.
For more information about technology and eye care see:
3D Printing and Optometry