I'd argue that Machiavelli didn't really believe much of what was written in The Prince. First, Machiavelli, aside from in The Prince, was a very consistent supporter of republican government (contrast, eg his Discourses on Livy); also, he held several high offices in the Republic, and was fired, tortured, and sentenced to house arrest following the Medici return to power. Second off, much of his advice given in The Prince was objectively terrible, and would have increased the likelihood of a counter-counter-coup against the Medici- Mary Dietz gives a longer argument here (HT Gwern), which Wikipedia summarizes as:
(Even if it wasn't a trap, it's likely Machiavelli had severely compromised his own principles and ideas in The Prince in order to gain favor with the Medici.)
If I am not mistaken, Burnham argues in his Machiavellians: Defenders of Freedom that although Machiavelli believed republicanism to be generally the best form of government, he did not hold that republicanism was the best form of government for the Italian city-states at that time.
Having not read the article, I cannot criticize the arguments that it contains. However, I am inclined to say that it goes against the mainstream view of Machiavelli (that is, mainstream view of experts on Machiavelli, not just mainstream view of the masses).
In modern usage, the name "Machiavelli" is a byword for cynical, selfish scheming. In this post, a Renaissance scholar places Machiavelli the human being into historical context, illuminating that Machiavelli was not cynical so much as desirous of an accurate map of the territory, and not selfish at all but rather relentlessly goal-oriented. (The post starts slowly -- that's historical context for ya.) In writing Il Principe, Machiavelli (quite possibly unintentionally) committed to posterity two major breakthroughs, which we would now call (i) the creation of modern political science and history and (ii) the introduction of utilitarian/consequentialist ethics.
Consequentialism
In 1498, at the age of 29, Machiavelli was made a high official of the Florentine analogue of the State Department/Ministry of Foreign Affairs. His job was to shut up and do the impossible:
Modern Political Science