I don't find a specific non-functional requirement that says Swing technology is required. Also, I don't find a specific functional requirement that might best be met with a Swing-based design. However, I do think it is clear that we need to support both "web clients and application clients".
I interpret this to mean that some remote clients will communicate with a web server, some will communicate with an application server, or perhaps even some will do both.
My approach to requirements analysis has been to consider the few "clear requirements" in a way that is specifically addressed in the design. Then, to concider the many "unclear requirements" as justification to include flexibility, abstraction, extensibility, etc. A clear requirement deserves an optimized design, an unclear requirement might mean a more resilient design.