Okay, I have to admit, this one has me stumped.
Any game can be run as an "Intellectual" game.
"Intellectual" defined as: characters play investigative, brainy types, I would have to say Chill or Call of Cthulhu.
"Intellectual" defined as: psychological or cerebral...probably SLA Industries, because that is how I run it. Skirting the gunbunny and going crazy with supernatural, psychological and just plain weird events.
Now, if you define "Intellectual" as: you are required to be a subgenius to play it, I would have to go with Space Opera.
Still, I prefer to run all of my games on a more intellectual/psychological level than just "kill things and take their loot." That is fun, do not mistake my words, I love a good dungeon crawl, but for me there is a need for it to be just a little more than that.
Traps, puzzles, strange goings on, those are all more important to me than killing a big bad and looting a magic item, I can do that in video games.
In that light, every game I have is an "Intellectual" game. Even when running the fast-paced action adventure games like Star Wars or d6 Adventure I like to have a modicum of challenges that require the players to use their heads to get out.