To add to the answers given already, there's the matter of the sheer scale of wealth these people have (especially relative to e.g. median worker wages). The richest people on earth in the 80s were a bunch of discreet Japanese CEOs with 5 or 6 billion$ to their name. They were very rich, sure, and surely could influence politics with their wealth.

But Elon Musk has 850 billion dollars. That's 850,000,000,000$. An amount so mind-boggingly impossible to imagine that you need analogies such as these https://www.youtube.com/watch?v=c96F7D57CzI. And these people got it not as a CEO of a quiet car company or such, but as owners of media and tech empires with a reach and influence Ted Turner could only dream about. It's a qualitative leap.