"Then I post a law professor who is highly regarded a constitutional expert, and all of the sudden 'quotes don't establish anything'"
No: all I pointed out is that the Volokh passage you quoted doesn't actually claim -- let alone conclusively establish -- that the U.S. is *not* a democracy, which is the claim you've been pushing this entire thread and have reiterated yet again. Curiously, because you again acknowledge what you call "democratic processes" of our system.
You've also set up the strawman of "direct democracy" and gleefully knocked it over again, perhaps not realizing that is just one particular form of democracy.
"Democracy" is broad enough to encompass representative systems of government just as we have here, and protections for minority parties as well.
The U.S. is a democracy. But don't take it from me, take it from the dictionary.