Can someone explain how activist investors are able to exert this kind of pressure ?

Activist investors buy themselves enough ownership to have a voice at or about a company, which they can then use to advocate for or against specific strategies, business decisions, etc. They often get involved when a company is doing poorly, and provide a sort of rallying point against the CEO, who is generally getting the blame from investors for the company's poor performance. The whole point is to influence public and/or leadership discourse about the company in their direction. In a cynical view, they're hecklers. Unless they buy majority control or can gain majority support, they can't FORCE any changes - but they can make the job of the CEO absolutely miserable until their demands are met. It's not surprising someone working under those circumstances would leave (especially when they have a billion dollars to go do literally whatever else they want).