Ging Mo Meng never did tell Seung Gwoon Gum Hung that he (Ging) was the one who killed Seung Gwoon Fei.
Were it most other people, I could completely understand the reason for not revealing oneself as the killer of Seung Gwoon Gum Hung's son (the retribution is sure to be horrific), but Ging Mo Meng has always left me with the impression of being one who is not afraid to own up to the things he does. However, when Seung Gwoon Gum Hung mistakenly identified Lee Chum Foon as his son's killer, and later seemed to even believe Ah Fei's false "admission" that he had killed Seung Gwoon Fei, Ging Mo Meng let Seung Gwoon Gum Hung live with that error.
That seems out of character for Ging Mo Meng in my view. He doesn't seem to be the sort to allow someone else to take the blame (and the punishment) for something that he did. His pride, if not his code of honor, would not allow for such a thing.