I got some idea from the MediaSelectionControl which also utilize the dialog.
mConfig = new DialogConfiguration();
mConfig.SelectableContent = SelectableContentEnum.OnlyMedia;
mConfig.OutputFormat = OutputFormatEnum.URL;
mConfig.HideWeb = true;
mConfig.ContentSelectedSite = SiteContext.CurrentSiteName;
With that, at least the media library shows up, but you are selecting a file from there. Not just a path (you may do some trimming to get the path as a workaround).
But if you look into our Media Library web part, you will see the way to set a path to a media library folder is actually to select the library, and manually entered the path. If we don't have the media path select option available out of box, I doubt modifying the DialogConfiguration will work.