In my rural school we were taught that the USA was a democratically elected republic, a hybrid of the two. Some republics the representatives are the wealthy, landowners, party members, or combinations of them and others.I went to high school in the early 1990s. If you called the USA a democracy my senior year government teacher would start yelling. We learned it was a republic, at least at my rural high school.
I have never thought of the USA as a democracy because I understand the difference.
By the authors standard China is a democracy. It has a constitution and elections.