Some of this is kept in the film - for example the ring structure. Some is discarded - for example the number of prose sections. And some is altered - for example there are just 12 ships, which come down from orbit to ground level... which does allow the very cool "each team has 1/12 of the whole" twist near the end. 

Does this just reflect the strengths and weaknesses of each of the two storytelling media? Or is something else at work? And most importantly, do you appreciate and respond to literary structures or not?

The best Planet Earth analogy I can think of is the use in certain ancient languages (eg ancient Egyptian or Akkadian) of written markers called determinatives. These indicate some quality of the word (eg "made of metal", "is a herd animal", "is a god") but so far as we know had no corresponding indicator in the spoken language. About the only similar feature which has survived into modern English would be capital letters to indicate a sentence start or proper noun - these help the reader to parse text, but do not have any analogue in spoken conversation.

Is there any connection with the extensive use of visual icons in computer and phone screens? (or road signs, for that matter)

Ted Chiang has recently released another collection of stories - are you tempted to get hold of it? So far as I know he has not written anything more than these two sets of short stories, and in particular has not developed an idea into a novel. Do you have any thoughts or comments about this? Do you think that Story of your Life could be developed into a novel or has it exhausted its potential at its current length?