It was true, but the oligarchs back then didn't constitute a single ruling party. It was more like Ukraine in 2000-10s, where you had several guys who are jockeying for power, controlling various political parties to contest elections, owning mass media outlets for propaganda etc. It's not your typical ordered Western liberal democracy, but at least so long as they fight, they have to pander to the people, occasionally; and the media, while not truly free, is sufficiently diverse to produce some semblance of truth in aggregate.

(Side note: Zelensky's "Servant of the People" is available on Netflix with decent subtitles, and I would heartily recommend it to anyone in the West who wants to understand the historical trajectory of former Soviet republics - Russia and Belarus especially, of course. What I found interesting is that, while it was targeted at contemporary Ukrainians in 2015-2019, the world that it depicts was very familiar to me from my memories of 1990s in Russia, aside from uniquely local issues like the languages.)

The difference is that one of Russian oligarchs decided to make a new political puppet with a "strong man" image. He was very successful, but then the puppet decided that it can make it on its own - and did so.