Echoing what some other people said here:
1. The diagonal distance is to the area SERVED. The purpose of this "service" is to get people out of the building. People to not reside inside walls (unless you are in an ancient Assyrian palace and fell out of favor), so you only measure the diagonal within the occupiable space. Some people will excluded built-in cabinetry against a wall; or on sloped ceiling spaces, they will exclude areas with less than 5' headroom as being "served" by an exit because they are technically considered non-occupiable. I don't agree with the latter approach.
2. The length of the diagonal in question does not directly correlate to actual path-of-travel within the space. It is a straight line between two exit doors, regardless of what obstacles are in that line; in other words, it is not intended to prescribe a real-world exit path. It is simply a rule-of-thumb, a form-based concept that was found to be generally agreeable and was eventually adopted as a code standard to be likely to produce a safe space. Remember, it wasn't that long ago that the UBC required 1/2 diagonal, with NO 1/3 exception for sprinklered buildings. What happened since then that magically made a sprinklered building actually safer with 1/3 exit diagonal in 2012 than, say, 1994? Well, the main thing that happened was that we all agreed to it.
3. With that in mind, it is a "straight line" (1015.2.1), and it is measured "BETWEEN" exit doors. I believe it is acceptable to measure to the closest edges of the doorways to meet the definition of the word "between". If the code intended for it to be center of doorway, it would have said it by now.
Again, this is NOT about measuring maximum path-of-travel to exit; it IS about location of doorways.
BTW, for reference purposes, right now I happen to be looking at a 1994 UBC "Q and A" code applications manual. The ICBO staff responded:
"The code does not specify whether one measures the exit separation between the center lines of doors, between the nearest jambs, between door knob to door knob, or between any other points. However, we are of the opinion that regardless of which of the three methods outlined in your question are used, the difference is so slight as to be unimportant..."