Hi and welcome
In order to turn that debate into something constructive you need to define the words Casual and Hardcore, if you guys can´t agree on what those really mean the discuassion is doomed in the first place. Those words as much as many people may hate them are commonly used to define what crowd of people games are targeted at. With Nintendos new gaming approach the discussion on what defines hardcore and casual has become more heated and complicated. If someone calls all new Nintendo games casual they are clearly being "fanboys" anothe fun word we can discuss at another time. On the other hand saying there are no casual games at all is also a little narrow minded. For me and many other gamers casual games (not a negative word) are mostly games that offer a short but fun gaming experiance and are often targeted at people who don´t play traditinal games witch take more time and effort to play. Of course there are large gray areas here but I think its save to day that games like Wii Sports, Guitar Hero, Singstar, Party games are casual games because they offer a short, fun and uncomplicated repeatable experiance... now many will say that they are hardcore Guitar Hero players... this may be true but does not change the fact that its a quite uncomplicated game (eventhough hard on highe levels) which offers short gaming sessons and is best played in a group of people... this is my definiton of Casual and I think its save to say many agree with it... Mario does not fid that description... someone who has never played traditional games that have gameplay that is established and has been fleshed out over many many years (what I would call Hardcore... because over the generations these games have established a hard core of fans) will not be able to pick up a Mario game and enjoy a short session.
Oh and everyone who only wrote a two line answer to your question is a casual poster at best and lacks the devotion and skill for hardcore posting... 
