Grozdanovski was remanded on bail without plea and will reappear in the Auckland District Court this month.
But Li and Xia failed to appear in court and warrants are out for their arrest.
Gambling by a group of people is illegal if they offer a prize of more than $5000 and turn over a profit of more than $25,000 for commercial gain without a licence. Private gambling not for commercial gain is legal.
If found guilty, the trio face a maximum of one year in jail or a $20,000 fine.
The owner of the Parnell townhouse, who did not want to be identified, said she rented the property to Li in 2012.
She only became aware the property had allegedly been used for illegal gambling when police called her on the night of the break-in.
"I didn't have any idea of what was going on there. Each time I inspected the property it was absolutely perfect, there were even kids' toys lying around," she said.
The break-in and serious assault are not linked to the gambling charges.
The Department of Internal Affairs would not comment on a case before the courts.