No, the engine license is all you need. For the designers, you simply assign them a security role in NPrinting that allows them to create/edit templates and have the designer client installed locally on their machines.
From there, the designer is launched directly from the web console.
Just the Server license is all you need. The license itself may have a restriction on the number of engines you can connect and the number of users who can be allocated the Developer Role. However, you don't need separate licenses for the Engine & Designer.