So, allow me to correct you in your misunderstandings...

First off, the word by itself is not indicative of a form of government structure, which "democratic republic" denotes. So, your confusion rests on your misconception of "democracy" vs "form of government structure".

When I say the U.S. is a democracy, I'm not indicating that it's a "direct democracy". But democracy means that the power rests in the hands of the people, where the people make the decisions, even if indirectly through representative government. Our freedoms and rights are what makes us a democracy, and the technicality of being a "democratic republic" does not change the main point that, the power belongs in the hands of the people. The actual form of government that a democracy takes doesn't change the fact that, we are, more than anything else, a country based on the principles of democracy.

Here's the simple, but accurate definition of "democracy":

a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections

See?!? Democracy can come in the form of "direct" or "indirect" representation. But, the power is still in the hands of the people. Clear enough?!?

Secondly, a business entity is not a person nor people, not directly.

But, there are people who start and own and manage those "entities", and whatever occurs inside and outside those businesses, affects the people inside and outside the businesses. It's people in that business making the decisions, as such, they are part of the process that determines the direction of a country. Corporations are a bigger determining factor in the direction of a country than government, and that's the way it should be. If corporations are made up of people, then they have as big a role in government as those same people would have as members of the general population.

If a corporation were to be an inanimate object, not involving people, then it would have no rights in society. However, businesses are people, and not exactly an inanimate object, and thus, whatever government does, with normal everyday policy and regulations, will affect people and businesses. Thus, it's the right of people in general, and people within the corporate world, to make sure that, whatever government produces in policy and regulations, doesn't affect them in a detrimental fashion.

However, when it comes to business, they do tend to have a bigger voice in government with lobbyists and funding influences. That's not how a "democracy" is supposed to work, but it's what has evolved because of the bigger role that government has assumed over the people and businesses and the country in general. But, if we were to be as originally intended under the constitution, the "buying" of special favor and of politicians wouldn't happen or even be allowed.