Sure, they can (and probably do) use clustering and fail-over redundant servers. However, there are multiply layers that can become bottleneck. It is one thing to handle the incoming connections in the web server layer, but your DB also need to be able to handle the connection numbers , or you need to use multiple distributed DB servers too. Then you may hit the bottlenecks of the network switches and routers. Large server farms like Google need to build up redundancy and distribution at every level.
Based on the WHOIS record their website seems to be hosted by Akamai:
https://www.akamai.com
This is a cloud service provider, so they could have a service agreement with them to grow the service on demand.