Who are the "Non-Evangelical Protestants"? I think this is an important question, because there is this group called "Non-Evangelical Protestants" that research articles may use in order to distinguish them from "Evangelical Protestants" and "Catholics". 

I have a hunch that they are "American Mainline Protestants".
You are correct in that "mainline Protestants" is the largest non-evangelical Protestant group in the U.S.  Wikipedia states that "The 2004 survey of religion and politics in the United States identified the Evangelical percentage of the population at 26.3 percent while Roman Catholics are 22 percent and mainline Protestants make up 16 percent."

See this Pew Forum survey appendix that classifies various Protestant denominations into three traditions, "evangelical Protestant churches, mainline Protestant churches and historically black Protestant churches."