There is is indirect way, were people vote for a form of parliament (the legislative) that then passes laws, and then there are systems, Switzerland comes to mind, where people vote directly on laws. Both approaches are equally democratic.
I cannot be the only one that sees politicians promise things and then spectacularly not deliver when they get elected. If the folks you vote for don't do what you want and you cannot vote for someone that does, there is no way for you to influence policy with a "democratic" process. For most people "just get elected" is not an option, because for that to happen you need to be rich, well connected and relatively well spoken.
Oh dear, you really argue that every single parliamentary democracy in the world is not actually a democracy because, what, they are parliamentary? Something else?
How exactly is that disingenuous?