ping
is a utility which sends an ICMP "echo request" message to a machine, who, if it is supported and enabled, will reply back with the same packet that was sent to it.
The website is being served by a webserver listening on TCP port 80.
These are two totally different services, and one, both, or neither could be enabled on any machine.
What you are probably seeing is that the machine you are connecting to has a webserver running, but has ICMP requests disabled. Also, any number of firewalls could exist between you and this box, any of which could be filtering out ICMP traffic.
In fact, recent versions of Windows disable ICMP ECHO in the default firewall rules. It has to be explicitly enabled.