Wreak means to cause damage or harm and is not a general synonym for cause. A riot is an instance of public violence or affray and not an act of damage or harm capable of being caused by a single person so you cannot wreak one. One can cause a riot (or start one, etc.) and one can incite a riot, which means to encourage others to riot.
Such things give a completeness to prosperity, and contribute elements of agreeable consciousness that are not dreamed of by that short-sighted, overheated vindictiveness which goes out its way to wreak itself in direct injury. The Mill on the Floss - George Eliot When he found that it was not locked it was like an insult. It was as though some enemy upon whom he had wreaked his utmost of violence and contumely stood, unscathed and unscathed, and contemplated him with a musing and insufferable contempt. Light in august - william faulkner "Your grace seems to be grating rather than caressing my hand; treat it not so harshly, for it is not to blame for the offence my resolution has given you, nor is it just to wreak all your vengeance on so small a part; remember that one who loves so well should not revenge herself so cruelly." Don Quixote by Miquel de Cervantes
No matter for now. I'm gonna do research to understand better the use of the word. Anyway... if y'all may give more tips about the subject, I'll appreciate. Thanks.
You may have missed my post, but it you read it you can see that all of your examples the subject is causing harm or damage, and a riot is not in itself "harm or damage" but is the act of a group of people. Vindictiveness and vengeance are acts that are perhaps a little more indirectly damaging or harmful, but generally lead to these results.