In this case, the cause of the accident is not the unsuccessful restart of the engines, but the previous act of shutting them down. And only a voice recorder could tell us, why the crew decided to do that when they were already positioned on (right) downwind, flying slowly at very low level in good weather for a visual landing.
Clearly not a situation anyone would wish to be in, but why did they go so far downwind? They appear to have been so well placed to join downwind for 21R. Notwithstanding their decision to shut an engine down while still airborne to try to remove the vibration, had they concentrated on the 'aviating' bit first I doubt they would have died. Furthermore, they managed to fly away from an unpopulated area into a built-up area. So lucky that no one on the ground was killed.