One must be careful in reading the word "democracy" as it has multiple meanings - and many writers will deliberately conflate and inter-change the meanings with intent to deceive.
One sense is the very literal Athenian democracy - which might be regarded as government by plebiscite. Here every significant public decision is made by a direct appeal to the people assembled, and is nothing more than mob rule. History teaches us that those of influence will make every appeal to the people at the height of emotional intensity, when the ability of the mob to reason is at it's lowest ebb. This is readily seen not only with The Terror barely a decade after Voltaire's death, but repeatedly over the next 250 years during, among others, the Russian Revolution; Mao's Cultural Revolution; and the Khmer Rouge's brief reign of terror.
In contrast to this are various forms of Representative Democracy. The best known examples of this form are the Westminster form developed in the United Kingdom and exported to several Commonwealth Dominions, and Constitutional Republic as developed following the American Revolution and failure of the Continental Congress' Articles of Confederation. The common thread to all Representative Democracy forms is the removal of power from the assembled mob, by having The People elect representatives to in turn perform the duties of government, both legislative and executive.
These flaws of Athenian democracy were well known not only to Enlightenment thinkers but to philosophers as far back as Plato. There is nothing peculiar to the Salem Witch Trials except the ostensible crime. Mobs in all times and all places have, whenever empowered, run rampant over the rights, property, and lives of everyone who opposes, or is believed to oppose, them. Kristallnacht occurred less than a century ago; above are additional more recent examples; and I'm confident the gentle reader can draw from memory numerous examples both more and less recent.
Examining one instance in conclusion, the American Founding Fathers were amongst the most outspoken and noteworthy supporters of "government of the people, by the people, for the people". Yet they deliberately modelled the American Republic's unitary executive after a European Absolute Monarchy "tempered" into the rule of a Platonian Philosopher King, through constraint, by both lack of Judicial and Legislative power and a hard term limit. They had a much higher esteem for George III than they did for his minsters and, rightly or wrongly, felt the need for their rebellion was due more to those ministers than the Monarch himself. They sought to deliberately break the Westminster union of Legislative and Executive authority, in a Prime Minister, into separate roles of President, Speaker of the House, and Vice President (as President of the Senate). That last rapidly proved unworkable, but the former remains today a key constraint on the President's executive authority.
So in the referenced quote it is not "representative democracy" that is despised but "Athenian democracy". The so-called Absolute Monarchies of Europe never were absolute. Those monarchs had allied themselves with the burgeoning middle class, who accepted increased royal taxation as the price to be paid for increased royal power. In exchange, those monarchs introduced Rule of Law that freed the middle class from arbitrary action by the nobility. This "enlightened absolute monarchy" is what Voltaire and others are espousing, which the American Founders attempted to cut from whole cloth, and which the Westminster systems have evolved into.
And as a final note: Men of thoughts and letters, of not just the Enlightenment but times previous and since, quite rightly in this author's opinion, have regarded "Athenian democracy" not as the triumph of Rule of Law; but rather as the triumph of its antithesis: unbridled tyranny, the tyranny of the mob: with the strength of its greatest member, times thousands, and the intellect of its feeblest, divided by thousands.