The thing that the video missed in its entirety is that the two are not mutually exclusive. Basically, we are both. Our form of government is a republic chosen by through democratic means. To follow along the lines of the clip, our republic is decided on by the majority.
This is largely the case in both design and practice through our government.
The problem is that this clip over simplifies things(probably to better reach its target audience) to a point where the reality doesnt fit into design, but more importantly, it completely overlooks some historical examples that dont fit into its overall agenda. Which to me seems obvious that they want to direct middle schoolers towards the GOP.
Someone could just as easily produce a 10minute video clip to fit thier agenda to be a bleeding hearted wussy liberal, because we vote for our representative in government rather than having them appointed in most cases.