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.

Kent finished second in Division Two last season and were not given a spot in the top flight after Durham were relegated because of financial issues.
Gillespie, who joined Kent as cover for Allan Donald in March, led Yorkshire to promotion from Division Two in 2012.
"For this whole squad, the world is their oyster," he told BBC Radio Kent.
"Kent have shown that they can do it and they can challenge to play in the first division.
"They play against first division sides in white-ball cricket all the time so the lads know they can do it, it's just a couple of things falling into place."

A group of employees from the Northern Ireland Public Service Alliance (Nipsa) union are in dispute with their employer over pay and job grading.
The grievance involves 12 higher executive officers (HEOs) at Nispa offices in Belfast and Londonderry.
In a statement, Nipsa said it was "committed to resolving this dispute".
Nipsa employees are not permitted to become members of the union they work for, but the staff involved are members of another trade union, Unite.
Unite representative Kevin Kelly said it was a long-standing dispute and he accused Nipsa's governing general council of a "failure to practice a standard of industrial relations that they would expect of their officials".
"My members are disgusted that their employer, who routinely challenges poor industrial relations practice across Northern Ireland, is acting in a manner which no employer would dare," Mr Kelly said.
"This dispute is resolvable if the will of the employer existed.
"It is therefore with reluctance and sadness that our members have been forced to take the ultimate action left open to them, that is the withdrawal of their labour".
The affected Nipsa employees are to hold a one-day strike on Friday 30 October and will then begin a work-to-rule protest from Monday 2 November.
Nipsa general secretary Brian Campfield said: "Nipsa is aware of the concerns of this group of its staff and has been involved in negotiations with their trade union, Unite, about how the issues in contention can be resolved to the satisfaction of both parties.
"Nipsa has advised Unite that it is committed to resolving this dispute and is presently engaged in further work which will hopefully settle any outstanding matters."
A rugby match has been held in honour of an off-duty police officer killed in Liverpool last year.
[NEXT_CONCEPT]
Kent interim assistant coach Jason Gillespie says they can challenge for promotion to Division One of the County Championship this season.
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Trade union staff are to take strike action against their own organisation, claiming it has been "acting in a manner which no employer would dare".