Edit: found a fix, if quitting iTunes isn't enough for the installer, you need to launch the Activity Monitor and manually kill the "iTunes Helper" process. What a pain.
This seems extremely half-baked. The App Store doesn't install Xcode, it just downloads an installer for Xcode, and ever-so-helpfully places it in LaunchPad.
After launching the installer and letting it run for many minutes, it silently popped up a window requesting that I quit iTunes for the installation to proceed. Besides being an insane request, when I do quit iTunes nothing happens. And if I double click on the iTunes name it launches iTunes. And on top of that, this request window isn't associated with the installer app, so I wouldn't even know it has anything to do with Xcode unless I'm not doing anything else on my computer.
And to top it all off, the installer has disabled all its buttons, so there's no clean way to quit it, and no way to get it to check for iTunes again.
This is about the lowest quality that I've ever seen Apple achieve; I hope that the rest of the dev chain gets more love.