That appears to be an assumption, and probably incorrect.
CX253 was late, arriving 23:39 : CX254 scheduled for 22:20 departed 01:06 just 2hr46 mins late. Therefor, from your own account, 27mins were lost enroute accounting for an arrival 3hr13 mins late. You have proven that it was not the late arrival of CX253 or the late departure of CX254 which caused you to be late.
It was the "extraordinary circumstance" enroute which consumed the 27mins, perhaps adverse weather or ATC, in any event unless you can you can show the plane broke down it wasn't CX. If I were CX I'd consider my case watertight.
As an aside, you mentioned they transfered others to an earlier flight, I think that's called courtesy, an effort to reduce the number of passengers inconvenienced at no cost, a flyer on a codeshare award would rank lower with any airline than status holders and full fare paying CX customers. More than reasonable.
Times & data from flightradar