There are people marching through the streets chanting, "this is what democracy looks like." They don rose-tinted glasses - projecting their mob rule fantasy of popular vote and pure democracy on our explicitly democratic republic.
Words have meaning. It's not misguided pedantry.
It's sort of like how functional programming can just mean "programming with pure, mathematical style functions" or more broadly it can mean the techniques associated with functional programming like pattern matching, currying, etc.
In this case, it seems to me that the intention was to use the most broad sense of democracy.
You can have democratic (e.g. Iceland) or oligarchic republics (e.g. Ukraine), all the way to dictatorships (e.g. Russia).
Being a democracy and being a republic are completely orthogonal.
[1]: https://scholar.princeton.edu/sites/default/files/mgilens/fi...
[2]: https://www.vox.com/2016/5/9/11502464/gilens-page-oligarchy-...