I don't know about the Liaoning but I remember back in the '80s or '90s hearing that the PLA ran what were essentially gun ranges where regular civilians could pay to fire anything from small arms to RPGs and AAA. Something like that I can see happening again as part of a PR or recruitment campaign, same with running a skydiving or off roading or wilderness survival operation. Nothing that risks giving away information on frontline equipment or advanced tactics though.
Back in 2008 I was able to do this kind of commercial shooting in Beijing. Went there with some friends and fired off hundreds yuan worth of assaultrifle rounds.