I don't think they wanted/expected him to quit. Figured he'd be okay with a loss of authority as long as he kept his office, title, and compensation. He obviously wasn't. My guess is that they are trying desperately behind the scenes to patch things up and convince him to return, and he's having none of it.
They're screwed.
This is not uncommon in the corporate world. The CFO thinks he is smarter than the CEO, plus he knows where all the bodies are buried. So he attempts some sort of coup. The CEO gets wind of it and fires the CFO. Then the board steps in and decides to oust the CEO and elevate the CFO to the CEO spot. Or not, depending on who controls the board. I have seen this very thing on boards I have personally sat on. In my case the CFO lost the battle and lost his job because a board member who had been encouraging him to instigate the coup turned out to be a spy for the CEO (no, it wasn't me). It can be a very treacherous business.