Put aside for the moment the question of why the Republic fell. Romans themselves had different ideas of what the Republic was, and when it fell. Modern scholars usually put it sometime around the time of Augustus, but Levick in a recent book has argued that the whole periodization we use for Roman history has to be reconsidered. Instead, let's work through the claims in this piece and see what's going on.

For most of its history, the Roman Republic was governed by old political families and reliable power brokers who knew how to keep the masses in line. Elections were held, but they were deliberately designed to give the capitalists and the aristocracy the lion’s share of the popular vote. If the Roman aristocracy, which voted first, chose a man for office, officials often would not even bother to count the ballots cast by the lower classes.

This is an old view of how Roman elections operated, very much along the lines of Cicero's Scipio Aemilianus in De Re Publica (who may or may not be a voice for Cicero's real thought). Some of the terms are anachronistic: "Capitalists" aren't really appropriate. In the Centuriate Assembly, the wealthier classes did vote first, and if the first two classes agreed on the candidates further voting wasn't necessary beyond finding one or two more centuries. Rome had very few men outside its noble families reach the highest office; I think Wiseman counted only 15 in some 1000 consuls that came from new families. Among those political families, though, competition was fierce. So this claim is recognizable if a little off.

It's old though. The assumption here is that the first two wealth classes generally held together. However, recently some have started thinking that for whatever reason the lower wealth classes were actively courted and elections were competitive even among the poorest citizens. Jakobson is the scholar I associate with this line of thought most; Lintott and Morstein-Marx also. If the lower classes were actively courted, it seems likely the upper classes were not as solid in voting the "right" way.

On occasion, disgruntled farmers, tavern owners and donkey drivers would unionize and rise up, pressing for debt relief and a real voice but these revolts were put down quickly with promises of better times ahead and by hiring a few police-gladiators to beat up the chief troublemakers

This point is hogwash. This could be conflating several things from the Conflict of the Orders to the unrest around the Gracchi or the public violence of the mid 50s. If the poster is referring to the Conflict of the Orders, that tradition is one of continuous expansion of rights and political access and religious participation to non-nobles, sometimes with violence or withdrawal of lower classes from the city. In tradition, these movements were successful, so that runs counter to the poster's narrative. "Union" again is a terrible word here.

The Gracchi did get beat up (both were killed with a number of their followers), but that wasn't easy nor did they involve the use of gladiators. Both the Gracchi pushed the aristocracy (well, "aristocracy" is also a bad word here, since the Gracchi were aristocrats and had aristocratic allies) for a couple years, both made the opposing faction think violence was the alternative, but [edit] neither set of opponents used hired gladiators for skull thumping. Scipio Nasica lynched Tiberius Gracchus at the head of a mob of senators, and Opimius made use of mercenaries.

Hired gladiators were used to thump skulls between rival political gangs in the late 50s, but those were not state-organized gangs, and the state only ended the violence by appointing a sole consul and a military occupation of the city.

The man who ultimately brought down the Republic was a wealthy and ambitious nobleman. Augustus guessed rightly that the ordinary people, long oppressed by the rich and powerful, sighed for the government of a single man, a man who would be the ultimate master, not the accomplice, of those petty tyrants The people of Rome, viewed with a secret pleasure, the humiliation of the aristocracy, and they demanded only bread and public shows; and they were supplied with both by the liberal hand of Augustus.

So Syme argued that Augustus overcame the old aristocracy by organizing support of the marginalized against it, but the marginalized in this case were other Italian aristocrats. Syme wasn't arguing that the common Roman on the street chose rule of one tyrant instead of rule of many tyrants; it was the Italian aristocracy that had little to no access to the political machine that chose the single tyrant. The Revolution, Syme argued, was the establishment of a new oligarchy to replace the old oligarchy. I don't know anyone that thinks there was a lower-class wave of disgust with aristocrats that Augustus rode into power. Augustus was the most aristocratic guy in town.

Why the Republic really fell I think we will be arguing over for a long time, but this poster's explanation isn't one that I think will get much traction.