As far as I know, AEM does not allow authors/users to "quick edit" uploaded files. You have to download the file, edit it, then reupload it. Can you implement this functionality or is it essentially impossible with AEM?
AEM doesn't provide that capability built-in. You could develop a component that uses a rich text editor, then use that to allow authors/users to edit a blurb of HTML. But that is still saving the rich text output as a property of a component in a page node and not saving the updates as a file, such as you have with a DAM asset. See https://helpx.adobe.com/experience-manager/6-3/sites/administering/using/rich-text-editor.html, particularly under the misctools description about how to "edit the HTML source" for more info on that option. You can provide custom asset editors (see https://helpx.adobe.com/experience-manager/6-3/assets/using/assets-finder-editor.html) but that doesn't allow the type of edit capability you are asking about.