Test post #2 is uncategorised, thus not subject to any controls. (The other test post there requires logging in to see.)
This smells of this bug where if the category isn’t changed, the post gets dumped into Uncategorised for admins even if such posts are not supposed to be allowed.
Unchecking allow_uncategorized_topics (which has been done on @nickjharrington’s site and mine ) normally should disallow non-admins from viewing, but doesn’t appear to in this instance…
For example https://what.thedailywtf.com/t/sign-here-please/48904 is in uncategorised on mine and shows the “You need to log in screen”"
http://magistrates.today/t/test-post-2-for-security-testing/56 on the other hand is also uncategorised but doesn’t require a login.
I can only think that there’s another site setting that I can’t find that’s different between the two sites…