Yeah, the more I look, every one in your list that's missing a favicon is actually missing the favicon on the site.
You can use the "alternate images" configuration in the plugin to give these another favicon instead.
The plugin assumes the favicon is on your site, but you could point to a full URL to a favicon you like. Maybe a CDN would be OK, but I'd suggest hosting it yourself, so you don't need to rely on someone else's favicon.
the configuration is simple: domain.tld:/path/to/favicon.ico
one domain/icon per line.
Here's an example: standpunktet.no:https://www.google.com/favicon.ico
Any link from standpunktet.no would be displayed with the google favicon (just an example, using the G might be a bad idea...)
The plugin has only registered e24.no as an excluded domain. Either your configuration only has that one domain, or there's something wonky going on with this plugin in the newer versions of Joomla. I haven't tested it since J3.1....I wrote it for someone - and I don't use it myself.
I'll have a closer look, and maybe release a new version to take advantage of the new form field types. That would make configuration much easier.