They don’t have rich people or corporations in Chile?

Not to be pedantic, but... both the US and Chile are representative democratic republics, not democracies.

Neither is an oligarchy, either. And while corporations and individuals of means have a disproportionate amount of influence in American politics, Chile is not immune from the same phenomenon; it just takes a different form.

But I agree with you in spirit - wealth should not be a factor in how much influence someone has in a democratic system.

This is not what anyone has meant by the term "democracy" for a thousand years.

To back you up, I can confirm that people who spend their time thinking a lot about this stuff (political scientists and those in related fields) spend zero time quibbling over the use of the term "democracy" as it's commonly used, and are likely to eye-roll and attempt to disengage from conversation should someone push their glasses up their nose and "well, actually..." the issue. In most contexts they use democracy as an umbrella term, the same way everyone else does. Doing otherwise marks one as an outsider to the field, or a novice—any in teaching positions get to correct plenty of "clever" freshmen on the issue every year.

I am an outsider to the field. I'll just disengage entirely from political discussion and leave it to the experts.