Denis Burakov, 27, was killed and friend Vladimir Shcherbov, 33, lies in hospital in a serious condition after climbing into the giant inflatable ball before being pushed down a skifield.
The video, posted online, shows the orb race to the edge of a rocky ravine, before disappearing down Ganachhirskiy Gorge at Dombai resort complex in the North Caucasus mountain range.
Local police spokesman Sergei Shuvayev told Agence France-Presse that a criminal case into "causing death through providing unsafe services" has now been launched.
The charge carries a maximum prison sentence of six years.
Mr Shuvayev said one of the ride's organisers, Ravil Chekunov, a 25-year-old local, had been detained and was being questioned by police.
Chekunov would probably appear in court later today to extend his detention, he said.
"This ride was organised illegally. At this height, in a high mountainous place, it is categorically prohibited to organise and hold such an event," Mr Shuvayev said in televised comments.
The video clip shows the two men inside the orb being launched down a groomed ski trail.
A man's voice is heard saying, in Russian, "Oh f***, it's gone in the wrong direction again," before it careers left and right.
A male voice screams: "Hold it, hold it! Hold!", and then "Ah well, it's OK, it'll stop by itself."
The ball disappears from view, the friend filming the ordeal asking: "What's going on there?"
"A catastrophe," someone says, and the clip ends.
The extreme activity's latest death could severely damage New Zealand's reputation as the world's adventure capital, says a disgusted Mr Akers.
He hoped that those responsible would face criminal charges.
Hope Horrocks, chief executive of Zorb Ltd, which runs the popular Zorb Rotorua site, described the death as "very troubling" and called for a global code of safe operations to try to stamp out rogue operators.
