Unfortunately on the nose. We do not have a representative democracy we have and probably have had an Oligarchic Republic. This only becomes more obvious as the Republic (power split down to and exercised at various geographic/social sub units) is over run by the federal (central) government where the oligarchs can focus their power to get the biggest bang for their bucks.
The confusion and purposeful distortion of the words/meanings of-democracy, representative-democracy, republic, federal…and others is probably more important than the issues with the presidency. The more centralized power is the more important controlling the levers on that power becomes.