So much Sugu and Yui fanservice.
Kirigaya Kazuto is the main character's name. He probably never told Sugu about what happened in SAO because A) she probably didn't want to ask, and B) he probably doesn't want to go over it. "Yea, I had to kill this guy because he was about to kill me. This one time I got 5 other people killed."
I've never gotten the impression that Sugou Nobuyuki is any kind of programmer. If anything he seems more like a corporate businessman/manager type. He probably couldn't code his way out of a paper bag.