I still don’t see a constitutional right to vote for president of the US.
republic n 1 : a government having a chief of state who is not a monarch and is usually a president; also : a nation or other political unit having such a government 2 : a government in which supreme power is held by the citizens entitled to vote and is exercised by elected officers and representatives governing according to law; also : a nation or other political unit having such a form of government Source: NMW
In the context of the United States, both definitions apply.
As with Amendment X, the Founders didn't think that every single thing/detail had to be spelled out in simple English in order that it be comprehended by posterity.