While the directors of Clownfish and CEQT admit visiting Infinity and then designing Odyssey in six months after that trip, they deny their mazes breach copyright, creating any misleading link between the businesses or are causing damage to Dreamtech's reputation.
The dispute is due to be heard next May over two or three weeks and ahead of it, Dreamtech applied earlier this year for an interim injunction against Clownfish and CEQT.
It sought the closure of three of Odyssey's sensory rooms, the removal of all floor to ceiling mirrors in another room, and of all mirrors and "infinite hallway" signage.
But Justice Mark Woolford denied Dreamtech the injunction, despite saying there was a serious question to be tried in the case.
The injunction could pose a "significant barrier" to the New Zealand businesses' ongoing trading, he said.
"I consider the greater risk of harm if the proposed orders are made sits with the defendants. Allowing an interim injunction would be highly likely to ruin their business entirely, over a claim which will require an extensive examination and comparison of the businesses by way of a long trial, and in which Dreamtech is suffering no immediate, irreparable harm," Justice Woolford said.
Dreamtech is appealing the decision that refused the injunction and applied last month for its chief executive, Queensland solicitor Deborah Kelly, to take the case.
However, the appellant court said it was concerned Kelly's close association with the company did not sit well with the need for professional objectivity.
It declined leave for her to represent the company on the appeal.