The application button is the name for the large button at the top left of the new Office applications.
As you can see in the two pictures below I have now added the button which operates by showing a ContextMenuStrip when pressed. The Office Guidelines indicate that when possible the application button should be merged into the window caption area. When that is not possible there should be an area above the ribbon tabs that acts as the location for merging.
At the moment I have not implemented the merging into the KryptonForm caption area and so you can see the alternative appearance here. Once I have added the ability to have context tabs and context titles I will then look at the merging functionality.