They're not rich because they built a company and bought their way into political power (which is how many Western billionaires are made) but because they had political connections and used them to capture state assets. The result is that they are dependent on the government for their wealth- if they piss off the President, they'll get thrown in jail or slipped polonium. So they ended up becoming unofficial conduits of government power.
In the West, it can end up being the other way around, with governments becoming instruments of corporate power.
Whether it makes sense to call both kinds of wealthy people "oligarchs" is up to you, I guess.