When asked if I completed 4 years of school prior to 1/1/16, is this referring to a completed 4 year degree?

Yes, the question is referring to a completed 4 year degree.

If you are working toward a four-year degree, you will meet the part of the definition of an eligible student defined as “has not completed the first four years of post-secondary education as of the beginning of the taxable year”.  The fact that you may have taken more than 4 years working toward the degree is not what is being measured.  The fact that you have not completed it yet is what is being measured.