As much as I hate to muddy the waters even further, but we really have 3 different types of windows to consider:
1. A tabbed browser window.
2a. A window associated with an "app" that uses the chrome.windows API to open a window of type "popup".
2b. An "app" that is effectively just a shortcut that is set to open in a (tabless) window.
3. A "v2" app that uses the chrome.app.window API.
Currently, if I recall correctly, the chrome.windows API has access to (1) and (2) (since internally (2) is just a browser window associated with an extension).
From a user's perspective there is almost no distinction between (2) and (3), even though internally they are implemented very differently and have very different security profiles.
As much as we would like to distinguish between "browser" windows (1,2) and "native chrome apps" (3), I don't think we really do that at all from the user's perspective on any platform. They can all be launched from the app launcher, the icons in the app launcher and in Chrome OS's shelf look the same, and while "browser" windows all have a titlebar, I think that is a subtle distinction from a user perspective.
So, FWIW, I think that the chrome.windows API should have access to v2 app windows. I would also like extensions that use potentially invasive apis like chrome.windows to have more attention brought to that when they are installed, but that is an entirely separate topic.