Okay, this is definitely it.
You can download the Firefox version of the extension here, rename it to .zip, unzip it, and browse the source code.
Inside, you can see that this code is injected into the main page using script insertion (e.g.
document.createElement('script') ... the code containing
plugin.setSuspendState appears to operate inside the host/parent window context, which is why it is caught.
Since the script file is loaded from Firefox's extension system / the user's hard disk ... might not be a surprise that there are no frames or additional context for security reasons. Just taking a guess that that's what's happening.
There is also a Safari extension on that website that probably operates similarly.