I don't tend to take people who appear to be mentally ill and harassing people at their word, no. I call the police and allow our legal system to handle the matter. Canada is a country of laws and due process and not punishment based on vibes and crazy shouting.
We don't ship schizophrenic people off to The Hague without doing a bit of due diligence first and as with most ridiculous claims people make whilst screaming in public, it's highly likely this person is full of shit and mentally ill so maybe The Hague is bit premature. People who actually commit these types of crimes aren't known to stand around in public shouting about them dressed like someone's crazy ass old uncle.
Capital punishment is, in case you are not Canadian, illegal and a non-starter here. We won't even extradite to places where it's legal unless they provide a firm guarantee that capital punishment will not be imposed (see United States vs. Burns - Canadian Supreme Court - 2001)
This video shows someone who needs to be hauled off in a cop car and likely submitted for a psych evaluation.