iKe works by running a K script, which includes both calculating static data and defining some selection of functions. It then calls K functions in response to various events- mouse clicks, key presses, etc. K programs define handlers for the events they're interested in and ignore everything else. The "draw" function is the only one which is strictly required, and it returns a list of tuples which represent some bitmaps to blit to the display. It and "tick" (if present) are called repeatedly and automatically by the system to permit animation and so on.
iKe is designed to be similar in usage both to the kOS "Z" windowing library (details are unknown, but there is one example program available to the public: http://kparc.com/edit.k) and Processing, a Java-based environment aimed at beginners and artists.
I'm suggesting that other APLs could be equipped with a similar setup to what iKe provides- export an APL module with some set of event handlers and at least a definition of a "draw" method, and then use some cross-platform UI toolkit to feed the APL events and render its results for the outside world.
Does that make sense?