PC Neil Doyle, 36, died after he and two colleagues were attacked near the Aloha Club, in Colquitt Street, on a Christmas night out on 19 December.
Three men have been accused of murdering Mr Doyle and are due to face trial on 22 June.
The match was played between Ormskirk Rugby Club and Merseyside Police's rugby team.
They were due to play the fourth Green & Blue game, named after the respective colours of the clubs, on 20 December but the match was postponed following Mr Doyle's death.
A post-mortem examination found the cause of Mr Doyle's death was bleeding around the brain.
Christopher Spendlove, 30, and Andrew Taylor, 28, pleaded not guilty to murdering the officer and wounding his two colleagues when they appeared in court on 20 March.
Timmy Donovan, 30, formerly of Huyton, has been remanded in custody after he was extradited following his arrest in Germany, in January. He is due to enter his pleas on 8 June.
Nearly Â£30,000 has been raised for a memorial fund in PC Doyle's name, with donations going towards Merseyside Police Federation Charitable Trust.
PC Doyle was based at Eaton Road station in West Derby, Liverpool.
A rugby match has been held in honour of an off-duty police officer killed in Liverpool last year.