He said "a hybrid of representative democracy and a republic" but these aren't remotely mutually exclusive terms. It is essentially a category error.

It's a bit like saying an electric car is not a car because it doesn't run on petrol, the fuel is not what makes it a car. If it's got four wheels and a motor, and drives on a road, it's probably a car regardless of what it uses.
Now if vehicle could only run on rails, then it's probably not a car at all but some sort of train, but trains can still also run on petrol or electricity. The system the vehicle runs on and the fuel are not mutually exclusive, you can mix and match different combinations because we've experimented with all sorts of vehicles throughout history the same way we've experimented with governments.