this is like a theory and practice situation. in theory this is conflict of interest issue possibly undermines objectivity and so on. in practice Nvidia thrives and the man is a substantial reason of this. removing him will be plain stupid from the point of view of the company's performance.
Company success has nothing to do with the conflicts of interest above though.
But keeping him potentially exposes them legally. If she ever accused him of using his authority to coerce her into said relationship (purely hypothetical), the board is now complicit in covering up legit criminal behavior. This is why conflict of interest policy exists.