Strange, there it is written that drag-and-drop between applications works only between LCL applications. I never knew that, and I don't know if it is really like that. My major applications do not need this feature, so I never studied it, although it looks interresting.
So basically if that is true to do drag&drop to/from non-LCL applications you would need to either extend the LCL to support it (implementing in each widgetset that you need via operating system calls) or use operating system APIs directly to do it.