The thing about video games is you have to treat them in a different light. Mario Kart is a party game and is a BLAST when there's lots of people around. I was never a huge fan of Halo and CoD either, because they seemed more like a shoot-many-things simulator to me. But games like Assassins Creed (mostly single player games, although some multiplayer games do a good job of this as well) is you need to treat it almost like a book or movie. The only major difference is it's interactive. Much like a movie connoisseur enjoys the aesthetic of a movie as well as the story, you have to focus on aspects like that as well. If you love the aesthetic of a game (say Fallout 3 for the post apocalyptic wasteland with bits and pieces of the 1950's) you'll find yourself enjoying the game much more. And then some games are less about all that and more about technical skill (SC, LoL, DotA, CS, etc) which tend to make good esports.

TL;DR: Treat games like any other art medium. Obviously you don't have to like them but if you treat them as a form of artistic expression you might see more appeal in them.