Explanation: When we in the modern day think of a republic, we think of a state for the people, not just a narrow elite. And this is, indeed, the meaning of the original phrase, res publica, which the Romans used for their own state. However, by the period of the Late Roman Republic, it had degenerated from a plutocratic-but-constitutional regime into a government in which the Senate, the lifelong oligarchal body in charge of executive action, formerly one piece of the elaborate systems of the Roman Republic, had become all-but-absolute, freely pursuing illegal executions and extrajudicial killings, reducing and ignoring the democratic functions of the tribunes as it pleased them, and in general being a bunch of aristocratic dickheads. This is, in fact, one of the main reasons why Caesar was able to amass such a following - to many of the poor, anything seemed better than being leashed and muzzled by the Senate.
As such, though Caesar absolutely was a dictator and not exactly inclined to restore democracy himself, it's hard not to cheer for the Senate being stripped of the power it once so gleefully stripped from the people.