Implement ExportFontStylesAsText property to HtmlExportSettings that allows exporting font styles as html tags.

Resolution: 

This issue is addressed in the new version of the control - RadRichTextEditor. Please use the new control instead the RadRichTextBox.  

You can use the following code snippet: 
HtmlFormatProvider provider = new HtmlFormatProvider();
provider.ExportSettings.ExportFontStylesAsTags = true;