Yes. Europe Does Produce Big Tech Companies.
blog.awesomezombie.com
blog.awesomezombie.com
I bet the average consumer these days associates SV with Google, Apple, and Facebook, not the abundance of technology firms serving enterprise or vertical markets.
Video games have this mystical ability to avoid being marked by its place of creation. Looking through my shelf for big names; Mass Effect & Dragonage (plus an obvious shit ton more beforehand like Baldur's Gate, Neverwinter Nights, etc) are Bioware - Canadian; Assassin's Creed (Beyond Goof & Evil, Brothers in Arms, Far Cry, Heroes of Might and Magic, Myst, Prince of Persia, Tom Clancy's ...'s) - Ubisoft Montreal (the second branch of the French game developer). It's kind of hard to go on without repeating the article, or filling the entire thread with a mere list of the dozens of game developers that dominate peoples minds when it comes to video games.
The biggest game company that comes to mind when I think American is Maxis, and beyond that it's EA - which incidentally hasn't been the sole producer of a game I've enjoyed in so long that I'm currently completely incapable of thinking of one.