The example I gave was of a preview frame in a web IDE. Another example might be a prototype / mockup for a new browser interaction paradigm (ie. one where each of your tabs/windows are presented spatially in a zoomable plane).
This could be achieved via browser extensions, but so could any other extended page behavior (like being able to access the filesystem). This is about discussing this as a cross-browser feature of the web platform.
I think something along the lines of “http://example.com is requesting permission to open other websites”, with a “more info” link and maybe text like “I trust this page” for the “Allow” button, could be enough. Most non-technical people I know would understand and reject “allow this page to open other websites” the same way as they reject “allow this page to see my location”.
That said, one of the things I’d look for in this thread is brainstorming ideas for more clear wording that could more effectively convey the potential dangers of allowing this permission (while still being concise enough for a one-sentence infobar, since users tend to ignore any warning longer than a sentence).