The server uses name based virtual hosts, i.e., several host names share the same IP address. You need to provide the Host-header so that the server can decide which virtual host it needs to connect you.
You can easily test the request from your PC before implementing it on the Arduino. For example on Windows start the command prompt and type "telnet myip.dnsdynamic.org 80". When the telnet session is established type the same lines as you would print in the Arduino, e.g:
GET / HTTP/1.0
Host: myip.dnsdynamic.org