Of all the terrible things that Yeung Hong had done, it was his killing of Au Yeung Hak that condemned him to death. Had he not killed Au Yeung Hak, he would not have feared West Poison Au Yeung Fung's finding out about it, and hence probably would not have stricken Wong Yung's poisoned soft body armor out of panic.
Still, of Yeung Hong's various crimes, the killing of Au Yeung Hak didn't seem to be such a terrible one. For starters, Au Yeung Hak was no saint himself. Had Yeung Hong not killed him, it's likely that Gwok Jing and Wong Yung probably would have at some point in LOCH (in fact, Wong Yung almost did with that boulder). More importantly, Au Yeung Hak had just tried to rape Yeung Hong's wife, Muk Lim Chi. In modern law today, if a man kills another man in a fit of rage after seeing that other man violating his wife, the killer is punished, but comparatively mildly. In most U.S. jurisdictions, for example, such killers are usually charged with only second degree murder or even voluntary manslaughter...and generally don't get the death penalty or life imprisonment (perhaps ten to twenty years in prison). The reason being that this crime, while inexcusable, is understandable enough to mitigate the punishment. Furthermore, Yeung Hong was a prince. I do believe that in most kingdoms, the penalty for attempting to rape a spouse of a prince would be death. Whatever else wrong Yeung Hong might have done, I think he was well within his rights (ethically and legally) to kill Au Yeung Hak at that point.
Not that this mattered at all to Au Yeung Fung, of course, and Yeung Hong did have other ulterior motives (i.e. becoming the heir to the White Camel Mountain martial arts legacy of West Poison) beyond merely avenging Au Yeung Hak's offense towards his wife, but it's ironic that the one "evil" act that Yeung Hong tried desperately to keep secret and that ultimately killed him was one that wasn't really that evil at all.