In another thread I made, a few people failed to understand that by 'Core' I wasn't referring to Hardcore. Most people I heard use the term lately (game journalists and bloggers) have also made this mistake. This is mostly because they both have "core" in their name.
While they mostly get the term from Nintendo. When Nintendo say's it they are using business jargon not gamer jargon. Core Gamer really means Established Customer to Nintendo. The Core Customers of Nintendo may or may not be Hardcore.
A Core Game is simply Nintendo focusing on what they do best as opposed to some new thing they're trying out. Nintendogs, Brain Age and WiiSports were new branches of their business. When Nintendo made them they didn't know if a lot of people would buy them or not. So to Nintendo they weren't Core Games.
Core is not supposed to be the opposite of 'Casual'. Animal Crossing may be considered 'Casual' but regardless it is also a Core game because they know people will buy them. Wii Sports Resort can also be a Core game because they know people will buy it.
So, eventhough Hardcore is an obscure term with no clear meaning don't confuse it with Core which does have a clear meaning.
