Only two ways appear to exist to do this: (1) Create an OBSE plugin, or (2) force Oblivion and the external application both to interact with a text file (which I think also would require an OBSE plugin...)
DragoonWrath, I'll definitely take you up on your offer for assistance. Please PM me when you have a chance so we can discuss details.
While I believe I could write such a plugin if given enough time to learn, and while I am willing to do so, this project could be released much more quickly if I could get some help! Would anyone be willing EITHER to:
(1) write the plugin that allows the Oblivion script engine to communicate (send and receive text) with the external application, or
(2) design the user interface (i.e. the chess battlefield in Oblivion) with some general guidelines I can provide.
Is anyone interested in either? Would it help if I mention I have an awesome idea for how to integrate this into an upcoming WEPON quest?