His colleague and another workmate who arrived shortly after tried to pull Randall from the water as he clung to a rock.
However, the force of the water ripped him from their grip and he was carried over the 11m waterfall.
His body was found submerged in water beneath the falls the next day after an extensive search and rescue operation, the report said.
A post-mortem examination confirmed the cause of death was drowning.
He also suffered a significant head injury which may have knocked him unconscious at the base of the waterfall.
Blood alcohol levels could have affected Randall's judgement and reaction time when he was running over the rocks at the top of the waterfall, the report said.
Coroner Carla na Nagara found the death was not the fault of any inadequate management of risk by the Department of Conservation (DoC).
"He chose to climb over a significant barrier, and then run down on to smooth rocks wearing skater-style shoes with no significant tread. It may well be his judgement and coordination were affected by the level of alcohol in his system, although his colleagues noted he did not seem particularly drunk,'' she said.
"I find Mr Randall's death was a result of an accident, attributable primarily to the choices he made in crossing the safety barrier and rushing down onto the rocks above the waterfall.''
She commended the steps DoC took to put signs up warning of the dangers of going to the top of the falls, saying they might reduce similar deaths in the future.