Similarly, I find discussion about people and/or relationships to be quite "intellectual" in nature because such topics deal with psychology, even if the people holding the conversation don't realise that's what they're engaged in and don't use "intellectual" terminology.
Despite that, I still do not find most discussions to qualify for the "intellectual" terminology... I do not label my discussion of "intellectual" when I am talking with someone. I never say "oh, let's have an intellectual discussion".