What is the code to use in config.esriaddinx in order to make a Button-Menu (like that illustrated below) when using ArcObjects?

What you are identifying in your image is a ToolPalette not a Button or Menu. So use the AddIn Wizard to create your Buttons that you want to see in the ToolPalette then create the ToolPalette and add the buttons by their ID. Below is some demonstration code to get you going.

<ESRI.Configuration xmlns="http://schemas.esri.com/Desktop/AddIns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<Description>Type in a description for this Add-in.</Description>
<Version>1.0</Version>
<Author>hornbydd</Author>
<Company>University of Southampton</Company>
<Date>30/06/2015</Date>
<Targets>
<Target name="Desktop" version="10.3" />
</Targets>
<ArcMap>
<Commands>
<Items>
</Items>
</ToolPalette>
</Commands>
<Toolbars>