We have a Government that exhibits Democratic principles but our form of Government is a Republic. We are not a direct-Democracy.
That means we have a democratic republic -- or at least, we are supposed to. And a democratic republic, although indeed it is not a DIRECT democracy, is a form of democracy. Representative democracy is still democracy.
There are only two reasons why the Founders avoided direct democracy. One, it was impossible to implement with the technology of that time. And two, it would have been a threat to the privileges of the rich and powerful. But the latter was also true of representative democracy, which they also avoided.
Direct democracy on a large scale is not possible without the Internet. Obtaining the consent of the governed is limited to the speed at which discussion, debate, and decision-making can take place, and at the turn of the 19th century required face-to-face discussion. That meant democracy was only possible by proxy, through representatives, who could all gather in the same big room and discuss matters, which the people as a whole could not. Nowadays, this technical obstacle has been overcome, but there is no blame to the Founders for not implementing what would not have worked anyway.
But they can be blamed for avoiding representative democracy in order to protect the privileges of the rich and powerful. That's an unworthy motive, and definitely not one we should continue to pursue.