They argue the lounge constitutes a substantially enclosed space, despite officers ruling that a wall of glass louvre windows made it open.
During a judicial review in the High Court at Auckland today, their lawyers told Justice Rodney Hansen the decision to approve the lounge was based on a "fundamental error" in the law.
Two enforcement officers, making separate checks, approved the smoking area using the open areas calculator, which factors in air quality and floor space.
After key figures in the case visited the Diamond Lounge, counsel for the charities, Duncan Webb, told the court those factors were not laid out in the legislation and said inspectors were relying too heavily on the calculator.
"There's no exercise of independent judgement here," he said. "When you give someone a spreadsheet and say, 'plug in these numbers', and a box turns red or green, the enforcement officer uses that as an absolute test."
Mr Webb later said the calculator was an "irrational" test, demonstrated by the fact that removing one gaming machine from the Diamond Lounge could change whether it was classed as 'open' or 'enclosed' because of the extra floor space.
Mr Webb also said it was "not at all clear" how louvre windows are classified under the law.
"When you look at that boundary of fixed louvres you are looking at an enclosing structure," he said. "They are there to protect people from looking in, to protect you from the elements to a degree, they are part of an enclosing structure."
Ministry counsel Joanna Holden defended the calculator which she said was developed as an objective tool to help determine what was classed as enclosed after initial decisions were too subjective.
Ms Holden argued that floor space was a valuable method of calculating how many people could be in a room.
Asked by Justice Hansen whether the test could lead to "incorrect judgements", she replied "potentially, yes".
But she insisted that officers used their own judgement when making their decision.
"The guidelines say the act is paramount. The calculator is one tool that should assist you to assess whether [an area] is substantially enclosed or not. You then look and use your own judgement and that has to be your decision."
Justice Hansen reserved his decision.