Usually mandatory for decisions about a board member for them to be recused. That there is an overwhelming potential for conflict between personal interest and the firm’s is pretty clear in that case.
Because it's a conflict of interest - a CEO should absolutely recuse themselves from a vote on whether they should be removed. If a CEO refused to do so, the board should adjourn and reconvene without the CEO present.
FWIW, radio silence from Ilya on twitter https://twitter.com/ilyasut