The crime happened in Canada, so Canadian law should apply. However the murderer fled to China where he was arrested... So Chinese law applies regarding extradition. It sounds like the Chinese and Canadian authorities worked out a cooperative arrangement, where the RCMP helped Chinese authorities prosecute the case in exchange for a guarantee that China would not seek the death penalty.
Since China had the killer in custody, in practical terms, they were in the driver's seat.
While this case is unusual, justice appears to have been served, which is more important than who gets to prosecute and incarcerate the offender.