Correct, an oligarch is part of a reigning elite. In any capitalist society where 10 people control more than 1% of the wealth of a country of 360,000,000 , those people are oligarchs. Let's leave aside that the list I describe includes people who control the majority of ecommerce and the internet cloud backend (Bezos), internet discovery (Brin and Page) and frontend (Zuckerberg) and work machines (Gates and Ballmer). 20% of the list is running private space companies to race to take over Mars or at least own space. One is even doing it as a hobby on the side (or was until recently.)

Musk bought a 9.6% chunk of Twitter because people say mean things about him on the internet when he says crazy things. And he's doing it for less than 1% of his net worth. That's an oligarch.