Democracy includes a broader array of governmental organization than just pure direct democracy. If you do believe that individuals should have some ability dictate the terms of their own social organization, then you believe in some amount of democratic principles.

Economic power eventually manifests in the political realm. The wealthy effectively get more votes, which means that society moves away from being democratic. Thus substantial wealth inequality is incompatible with democracy in the long run. We have been witnessing that corruption for a while now.