So, since Windows 8.1 there is undocumented flag PW_RENDERFULLCONTENT, which does the trick. But on Windows 7 there is no such flag, and I need to print window not in extension (so I can not use extension API or something like this), but from separate Windows application.
Anyway, is there a proper way to print Google Chrome window when GPU compositing is disabled? Maybe I need to disable something else? Is there a code printing to DC anywhere in Chromium? Maybe there is a way to call it? Maybe I need to hook something: I have read that PrintWindow() problem is related to asynchronous message processing, so hook message processing to make it synchronous?