It says "screenshots of themselves". The application is responsible for rendering the screen in the first place so it fundamentally doesn't need a permission.
Now, what could reasonably be a permission is "access the internet", but our overlords don't approve of that thought.
(Contrast this to web pages, which do not render themselves and thus can sensibly be blocked from screenshotting)
For an increasing plurality (possibly even majority at this point) of sites where the purpose is not purely to read text, this is effectively equivalent to saying "you can just not use the site."
Now, what could reasonably be a permission is "access the internet", but our overlords don't approve of that thought.
(Contrast this to web pages, which do not render themselves and thus can sensibly be blocked from screenshotting)