Artis Sterkis, 37, collapsed on the Peterhead-registered Starlight Rays.
He was taken to hospital by rescue helicopter after the incident in August 2011, but he never regained consciousness.
James Thores was fined at Elgin Sheriff Court after admitting a fishing vessel health and safety breach.
The £20,000 fine was reduced from £30,000 because of the guilty plea.
Starlight Rays featured in the BBC television series Trawlermen, and was performing stand-by duties for the oil industry when the incident happened in the Devenick field, 155 miles off Aberdeen.
An earlier Marine Accident Investigation Branch (MAIB) report said the pump's petrol engine ran for more than an hour in a compartment with no mechanical ventilation and little natural air circulation.
Speaking after Thursday's sentencing, Captain Bill Bennett, of the Maritime and Coastguard Agency, said: 'The dangers of using of a petrol engine in a confined space are well known."

Enninful, who has previously worked for Italian and American Vogue, will take over from Alexandra Shulman, who announced her departure in January.
Condé Nast International's Jonathan Newhouse said Enninful was "an influential figure in the communities of fashion, Hollywood and music".
He is currently the fashion and creative director at W Magazine, where he has worked since 2011.
The 45-year-old will start his new role on 1 August.
After the news was announced, designer Marc Jacobs tweeted: "Congratulations to our longtime friend @Edward_Enninful, the new editor of British Vogue! We can't wait to see what you do! ❤️"
Caroline Rush, chief executive of the British Fashion Council, told the BBC: "Anything that promotes diversity and gender equality in the industry is incredibly important, but there's no doubt that Edward's been appointed because of his talent."
"He brings a very distinct point of view in terms of the imagery that he has been associated with, and I think that's going to be really exciting to see how that is translated into the pages of Vogue."
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A fishing boat skipper and owner has been fined £20,000 after a crewman died from carbon monoxide poisoning while trying to pump out water.
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British Vogue has confirmed Edward Enninful as its first male editor.