I don't believe this overall question has been addressed on the forums, but how did the European hereditary monarchs get to be kings, princes, dukes, grand dukes, etc?
Napoleon is usually criticized for becoming Emperor of the French from somewhat humble beginnings as a Corsican minor noble and beginning to rule as a monarch.
He was a self-made man who began as a soldier, a sword, and became the head of state of France in 1799 beginning as First Consul and then becoming Emperor of the French as well as King of Italy and Protector of the Confederation of the Rhine.
How did the Hohenzollerns, Hapsburgs, and Romanofs begin and then become kings, king/emperors, and Tsars?
Did they not have to begin somewhere?

It would be interesting to know what Andrew Roberts' intended purpose might have been in referring to the Gordon Riots of 1780 when discussing 'XIII Vendémiaire' of 1795 (in old money). As a quick scan of the linked material makes clear there was no comparison between the peaceful meeting at St Peter's Field in 1819, set upon by the troops supposedly acting in support of the civil power, and the rampaging mobs of 1780 shot down by troops when martial law was introduced after a five-day rampage of looting and burning the length and breadth of the capital. The two events are linked only by each being unprecedented in its own way and by the incompetence of the authorities in each case. They were also both political events however and it is true that the events of June 1780 instilled in the British establishment a deepening fear of 'mob' violence, only accentuated by the events of 1789 in France. Violent protest was seen as merely a demonstration of the base instincts of the common people which required control with force, rather than as a reaction against inequality and incompetent, repressive government, demanding reform. That self-serving complacency led inevitably to the criminal mismanagement of the meeting in Manchester, although these were both extreme events. There were for instance outbreaks of rioting between 1793-95 in London and the provinces which did not have such bloody results.