The issue of extraterritoriality applies only to the state torture, because the convention is trying to create an international regime. If the state does not abide by its obligations, does not prosecute someone who committed torture in its territory, and that person comes to, say, Canada, then Canada can undertake the prosecution and ensure that internationally there's no impunity. That is why within the convention there is this element of extraterritoriality.
For private conduct, we don't have extraterritorial jurisdiction, except in limited circumstances where there is an international treaty that requires it, or there's clearly a customary international law with a requirement or permission for a state to have that.
If I assault someone as a private individual in France and I come back to Canada, then I can't be prosecuted for assaulting someone in France. However, if an official in a foreign country tortures someone, and that official is not prosecuted in that country, then other countries are entitled to step into the shoes of that country and say that just because they are going to grant impunity doesn't mean the international community will grant impunity.
There are significant differences between the levels of conduct. Domestic conduct is about protecting the victim. It's all about saying that this person suffered harm and that we want to protect that person from harm. The international offence says that yes, we want to protect people from harm, but we also want to hold states accountable in that they should not let this happen, and that if they do let this happen, we're still going to ensure that justice is done by ensuring that we will prosecute. It's serving two different purposes.