While testing a bunch of EAX games and updating our wiki page, I came across some interesting things. First, this EAX Quality Assurance document:
The attachment EAX_QA.pdf is no longer available
It was originally downloaded from here but I'm attaching it to this post as well, in case it gets lost to time. That document seems to be from 2003, so it's missing some EAX 4.0 and EAX 5.0 functionality, but it's still an interesting read. Basically, it describes how game designers and their QA teams used to test EAX during development.
Next, there's EAX Unified. The latest standalone redist that we currently know of is 4.0.0.1 and it can be found on this page of the PC Gaming Wiki. Note that some later games ship with slightly more recent versions of eax.dll but I haven't found a newer standalone installer. Anyway, it seems EAX Unified was initially developed around the year 2000 as a bridge between EAX 1.0 and EAX 2.0. Final Fantasy 8 ships with version 0.0.0.1 which is probably the earliest release.
Later versions of EAX Unified were used to ensure that sound cards which only had EAX 1.0 and EAX 2.0 functionality (e.g. SBLive and most on-board audio solutions) could be supported more easily by developers who used higher EAX versions (e.g. EAX 3.0 and EAX 4.0) in their games. From what I gather, EAX Unified sort of "translates" higher EAX versions to lower ones. A few of the more advanced effects might be lost, but it seems to work ok for the most part. So later games could be designed primarily for EAX 3.0 and EAX 4.0, but thanks to EAX Unified, you could still get some of that functionality even on less capable sound cards. Pretty neat.
Lastly, certain games like Tomb Raider: The Angel of Darkness require EAX Unified to be installed, otherwise they won't have any EAX support.