That’s simply untrue. The Republic was on it’s last legs well before Caesar became Dictator. Marius and Sulla, though unintentional, did as much to undermine the Republic, not to mention Crassus and Pompey but it Octavian who put “done” to the Republic by creating the Principate.
Which is irrelevant as Rome, under the Republic, would have completely imploded by the end of the first century due the constant civil wars. Rome as a great Empire would have ceased.
So though Caesar contributed significantly to the fall of the Republic the Republic probably needed to be killed anyway and Octavian killed it permanently and gave Rome what it desperately needed. A strong executive government.
Caesar attempted that but screwed up by alienating the Roman political class by, as Doctor, essentially eliminating the Roman political institutions which the political class viewed as their birthright and they killed Caesar for that.
Octavian didn’t make Caesar’s mistake. He kept the Republican political institutions and permitted the Roman political class to compete for those offices but he legislated all real political power into the office of the Princips.
Which was political genius. He gave Rome the strong central executive it needed while preserving the prerogatives of the Roman political class.
And Octavian died an old man in his bed, unlike Caesar, and Octavian grew Rome to an even greater extent. Not only that but he created a stable political system that lasted over a thousand years into Byzantium.