I agree that Pike's retrospective of his alternate life was a good idea to explore - its the kind of thing that older trek series would quickly shuffle on after that week's episode (like O'briens stint in virtual jail). Pike has done a lot of thinking about coming to terms with his vision of his own future, so thinking about his alternate future was a necessary next step.
I just wish it had been given a better story in which to bubble about. If it's a serious character point, let it be told in a serious story. Let us see his job as a captain of a discovery-science-diplomacy ship lead him down that path of self reflection. Adding a comedic glamour filter on top of everything, in my opinion, cheapens the end result. It bugs me that so far we had erica/scotty needing to be drunk to learn to get along, spock needing to be dreaming / nightmaring, and now pike and co. stuck in a Q game in order to grow as people.
I actually had no idea who Deidre Hall was, though from the visual language I got the impression she was meant to be "someone important". I assumed they had picked a random actress and were making a meta-joke about guest actors on TV shows. I was half expecting her to vanish at the very end.