Thank you for correcting this. A further correction: when he ran his first 12:58, he was the 8th fastest runner of all time, not 9th. For anyone else who wants to do research, here is the WA top list for 5000m. There are two controls to pay attention to.
The first is the "Best by Athlete" or "All" buttons control whether you count athletes, putting BK 9th at the time, or performances, putting him 18th, at the end of 1996.
The second is the date picker. You can choose your beginning and ending cutoff days. And note that it's a day, not a year. McRunnin was careful to mention the end of 1996. If you choose that (31/12/1996, they use DD/MM/YYYY) then you get the rankings mentioned above.
But if you pick the day of BK's first sub-13 (it was July 8, so enter 8/7/1996) then you see he was higher ranked earlier in the year (8th fastest man of all time, 13th best performance) but a few fast races later pushed him down (including his 12:58 race, there were men ahead of him there).