Mr Wu did not report this incident, which was considered a serious breach of the rules, the authority said.
The authority said Mr Wu acknowledged the player's conduct was a serious breach of the game rules, he said he had been preoccupied and too busy to report the incident and that he had made a mistake.
Surveillance manager for Sky City Bill King became aware of the incidents the next day and reviewed surveillance videos, where he saw the incident that Mr Wu had not reported, the authority said.
Mr King said the incident was serious as there was no way to know whether the card that had been taken and returned to the table was the same card, the authority said.
At a meeting, Mr King questioned Mr Wu on the incidents and although Mr Wu admitted to the first incident, it took some time before Mr Wu mentioned the second incident, which he said he did not think was suspicious, the authority said.
Mr Wu was then suspended on pay while further investigation into the incident took place.
A meeting was then scheduled but Mr Wu asked to change the time of the meeting as he had an exam on that day.
Mr Wu said Mr King refused to change the time of the meeting but Mr King denied this, the authority said.
At the disciplinary hearing, Mr Wu attended without support or representation but said he was happy to proceed without a support person, the authority said.
Mr Wu's managers told the authority that they were concerned he did not understand the serious nature of the meeting, and said they called an employee support adviser to meet Mr Wu and explain the seriousness of the situation to him.
The support adviser told Mr Wu that he could allow the disciplinary meeting to continue to an outcome and then consider his options, or resign before any outcome.
Mr Wu asked the support adviser to confirm that he would not have dismissal on his record if he resigned, before saying he had already been offered a job at another casino, the authority said.
Mr Wu then resigned from his job, although he later told the authority he said this "to save face".
Although Mr Wu claimed his resignation was a constructive dismissal in which the circumstances was unjustified, authority member Anna Fitzgibbon said she did not believe this was the case.
Ms Fitzgibbon said Mr Wu was given notice of the disciplinary meeting and was fully informed of his rights before attending the meeting.
She said he was given the opportunity to adjourn the meeting and obtain legal advice or a support person but did not do so.
"On the balance of probabilities, I find that Mr Wu resigned and the resignation was not a constructive dismissal," she said.
"Even if I am incorrect, it is my view that Sky City carried out a full and fair investigation and determined Mr Wu's failure to report the second incident constituted serious misconduct for which dismissal was appropriate."
Ms Fitzgibbon encouraged both parties to agree to costs.
Nathan Santesso, who appeared as an advocate for Mr Wu, said Mr Wu was a good employee with no previous disciplinary issues.
He said they were both disappointed with the outcome and would appeal against the decision in the Employment Court.
Sky City general manager for corporate services, Grainne Troute, said the company was always confident with its position.
"We are pleased that the court has recognised that our processes were sound and fair."
