A video posted on YouTube by Kaduguda shows the large bodied aircraft taking off hardly halfway through the 1,620m length airport. In the video a voice is heard saying in Swahili that the aircraft lifted off "...at seven hundred" indicating that the pilot used roughly 700 metres of the runway to get this large aircraft off the ground.
Apparently, the aircraft did not have enough fuel to reach any of these three larger airports and the pilot diverted instead to the nearest but shorter airport in Arusha. News reports revealed that during the emergency landing the Boeing 767 slightly overshot the runway. No casualties were reported. The runway's length at Kilimanjaro is 3,600m.
The pilots are credited for both landing and taking off with such a large aircraft on a short runway. I believe the landing was much more difficult than the take off.