That search expression is correct.
You're searching for the word "site" and the word xenmediagallery.com.
The correct search term to see content for a single site is site:xenmediagallery.com
(The space makes it search completely differently).
My results:
Not a single notice appears there.
However...
You searched for
site and
xenmediagallery.com.
So, Google shows you the text it finds on an indexed page that is relevant to those two terms. It even
bolds them in your search results because that's what you searched for.
The cookie notice has the word "site" in it, so obviously it will show that because it appears on every page.
Here's some more results searching for the word "upload" using the expression site:xenmediagallery.com upload
Not a single result has any notice in it, yet there are notices that show on every page. It doesn't show the meta description, it doesn't specifically show the notice, it doesn't show anything other than what you searched for.
The only exception to that is where it cannot ascertain anything specific based on your search term it may choose something itself to show. That may be the forum description, it maybe some other text such as a notice. But the important thing is, in normal conditions, your users are seeing the content they're searching for. Nothing else.