It's his personal life...you aren't hired or evaluated on the basis of being in a relationship, cheating or not cheating etc so it shouldn't be a basis for resigning either.Youre often hired in part based on your personality and the way you present yourself. And when youre CEO, you represent your whole company.
Seems hypocritical too. There's more people out there cheating or not being faithful than you think and they're still at their job.