Northern & Shell also claimed Allwyn was allowed to modify its operational plans for the National Lottery after winning the contract.
Allwyn has said the changes were caused by delays resulting from the legal claims brought against it and the regulator.
However, lawyers for the Gambling Commission claimed Mr Desmond’s bid to run the National Lottery performed “extremely badly” and was “fanciful”.
Sarah Hannaford KC, representing the regulator, argued Northern & Shell’s attempt failed on several “mandatory” tests and “scored much lower” than Allwyn’s competing bid during the procurement process.
“It didn’t fail by just a bit,” she said.
In a legal filing, the regulator said Allwyn scored 87.18pc in the process, while Northern & Shell’s effort failed to pass several mandatory checks and was scored 57.5pc.
Because Northern & Shell failed the “pass or fail” assessments, the regulator argued its claims should be dealt with at a short trial as the group “cannot show that it could have won or that it has lost a real (as opposed to a fanciful) chance of winning”.
She added Rothschild were “not the decision maker” in the bidding process, but provided some financial analysis for the regulator.
It is understood Rothschild conducted some work for Allwyn in 2019, before the Gambling Commission process began.
Allwyn is owned by Mr Komarek’s KKCG, a holding company that has been scrutinised by MPs for its links to Russian energy giant Gazprom.
Its business includes a Czech gas storage plant, which was a joint venture with the Russian business.
Last week, KKCG confirmed it had bought out Gazprom and the facility now had no Russian ownership.
“This has been achieved after passing through a number of necessary legal and regulatory processes,” the group said, adding it prevented the plant from “coming under Russian control”.
A Gambling Commission spokesman said: “We are confident that our proposals that are being brought before the court represent the most effective way to dispose of the litigation.”
Rothschild was contacted for comment. Allwyn declined to comment.