"While this was an impromptu game among friends, not a planned event, this tragic outcome does highlight the inherent safety concerns with such an activity."
He added that it was not a police matter, but officers would "continue to undertake enquiries on behalf of the coroner".
"Run it straight" has long been played casually in Australia and New Zealand, but has recently taken off as a trend online and been endorsed by some professional rugby players, despite critics warnings it could give players head trauma and brain injury.
On social media, "run it straight" challenges show young men and students charging at each other as their friends watch on. In some videos, participants are seen passing out after being hit.
As the popularity of the game grew, some have started to hold their own tournaments - though it is unclear how these are regulated.
One such tournament, the Runit Championship League, made its debut in Auckland this month after first being held in Australia in March.
On its website, organisers described the game as the "fiercest, new collision sport".
The league drew more than 1,000 people to the Auckland's Trusts Arena as men went head-to-head for a prize of around $13,000 (£9,500).
Some participants were injured during their matches, and one video showed a man appearing to have a seizure after colliding with his rival.
But Runit Championship League organisers have promised to return to next month with an even bigger prize.
Kimami Ngaluafe, the organiser of Up the Guts NZ, another "run it straight" event in New Zealand, tells says the game has long been popular in the country, attracting five-year-old boys to men in their 40s.
"It's a Kiwi national backyard sport. The boys are currently playing as we speak," he tells the BBC.
But Satterthwaite's death is a reminder of how important safety is, Mr Ngaluafe says. He adds that players should wear protective headgear - which many currently do not - and have spotters around to prevent their heads from hitting the ground.
"In New Zealand, kids are playing this kind of game every day. They deserve to be guided properly and shown how to do it the right way," he says.
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