If you refresh the stats page, you can see the TCP stats updating just fine but the ICMP does not.
Guessing ICMP is just getting filtered at some point.
There's a much larger than zero possibility something (network gear) North of this thing is black-holing ICMP echo and/or your ISP is dropping the responses.
The site's IP is announced by https://www.blix.com/. It's conceivable that an IBM 5170 is sitting on its side in a colo rack, with a transceiver bridging its Ethernet card directly to the ISP's network connection.
But it seems more likely traffic is being forwarded or even rewritten at Layer 4. I don't think running something like HAProxy in non-caching mode would invalidate the website's claims. Even an IP forwarding solution (eg a GRE tunnel) might have http://shouldiblockicmp.com/ issues.
The other counters on the page are updating after each refresh. I think only the ICMP counter is broken. The IP address points to a Norway provider. I do not think there is a CDN, elsewise the counters would be frozen.