That "author" did NOT think non-propertied White men, Black men, women, or Native American men could vote. Those things didn't happen fully until 1856, 1868, 1920 and 1924 (though for Black folk didn't really happen until 1965).From a legal perspective, the interpretation of a legal document will be conducted by way of the author's intent.
Intent involves defining.
I can concur with the term constitutional republic. That is most descriptive of this form of government of the several States and of the United States.
That "author" did NOT have a system with the direct election of senators. That didn't come until 1913.
That "author" did NOT have a popular vote for the electoral college in every state. That wasn't fully instituted until the 1860s.
So again, it's meaningless to claim that someone from the 1700s is supposed to be the end-all for defining the name of a system that they were never even part of.