Texas, I think I'm going to let you have the last word on this. You and the author of the article you cited obviously care a lot more about the semantic difference between "democracy" and "republic" than I do. I'm going to stick by my argument that the government is defined by the US Constitution, and if you care whether the US Constitution describes a "democracy" or a "republic," then I will let that be your personal pet peeve.

It sounds like maybe your real concern is that your rights have been infringed in some way. If that's the case then I would suggest you get at the point in some other way than to argue whether the US is a "democracy" or a "republic." Your point is being buried under an argument about semantics.