What is the term for the discipline of dealing with the diagnosis and treatment of defective eye coordination, binocular vision, and functional amblyopia by non-medical and non-surgical methods?

The correct answer is orthoptics.

Orthoptics is a profession of eye care that do things such as diagnosis and non-surgical management of strabismus (wandering eye), amblyopia (lazy eye) and eye movement disorders. Orthoptists are trained professionals who are uniquely skilled in diagnostic techniques.