score:11
Having tested with, I think, the same availability checker you used to create your image, I am now very confident that your problem is that you're trying to reach
http://esta.cbp.dhs.gov
That, indeed, will not work. Instead, use
https://esta.cbp.dhs.gov
You can add https://
in the I want to test box, and the test will succeed. Apparently, entering a bare domain name results in an HTTP connection attempt. The ESTA server does not respond to these, but it does respond to HTTPS connections.