I hear web apps have landed in 12.10. I can't seem to get them to work in Kubuntu 12.10, however. Will they be coming to Kubuntu? Or did I just not set them up correctly?
No, it's a feature of the Unity desktop; you'll only see this integration when running that. (Which is why it says 'Unity Webapps' all over that article you linked. ;)
I don't know what KDE or Kubuntu might do in the future, but the new webapp integration code, that I know of, is largely Unity-specific. It's code to make the Unity Launcher, the Unity Dash, Unity's alt-tab switcher, Unity indicators and notifications, aware of web sites. When you visit sites from that growing list, in Firefox or Chromium, those parts of Unity can treat that website like a first-class citizen of the desktop.
This kind of integration may take off, and be built into more desktops in the future, but what you're reading about for 12.10 -- no, that's just Unity.