In a situation like this, we'll probably never know the real story. Nevertheless, I think we can draw a few fair inferences.
First, he absolutely violated the company policy. In a serious way. It is inconceivable that this happened without an investigation, run by outside counsel, that spoke to the woman who was involved in the relationship, him, and everyone else who might have known anything about it. If the board replaced the CEO without an outside investigation that covered all the bases, frankly the board needs to be replaced (whatever the truth about the CEO or anything else is).
Second, what the investigation found was troubling. Enough to justify firing someone. Maybe the woman felt it wasn't entirely consensual (though probably not, or Intel would have said something else). Maybe her coworkers felt she obtained unfair professional advantages from the relationship. Or maybe this came out some time ago, they were told to stop and they didn't.
Third, for the reasons well known to active participants on these forums, the board had lots of reasons to be troubled by his recent performance. There is a lot to criticize Intel about recently. This kind of issue is like anything else that's not an on-the-spot firing offence: are you a superstar that everyone wants to keep? They'll cut you some slack. Are you already on thin ice? You just fell through the ice.
Fourth, the board felt their hand was forced at least a little. This is an awkward situation that raises lots of questions (obviously, including all of the ones raised on this thread already). If they thought they could wait, they'd do a search and have a new full time CEO announced, not an interim CEO while they searched and made a definitive decision. That could raise its own questions, but this is a bit of a PR fiasco. No one asks for that unless they feel like it's their best option.