There are some who advocate this approach in the literal sense - two physical firewalls (perhaps even from different vendors). That is less and less often seen and has its roots back in the 90s when firewalls were less trusted than today - mostly stemming from some vulnerabilities found in some early firewall code.
Another way to interpret the diagram is logically - the flow comes in via an Internet-DMZ zone pair and then goes via a DMZ-Inside zone pair to reach the internal backend servers. That's not at all uncommon as it's just separate set of rules on one physical firewall (or cluster).
It is also sometimes implemented via the second "firewall" being a proxy server like a load balancer, perhaps with an application layer firewall function residing on it. In such a case, traffic comes in via, say an ASA outside interface where it is checked against an ACL and un-NATted to a load balancer VIP residing in the DMZ. The load balancer perhaps decrypts SSL and runs the http content through an application firewall before handing it off via separate interfaces to the backend internal servers. This is often done in things like e-commerce application where much of the content may be encrypted and we don't want to (or are unable to) put the load of SSL decryption on the Internet-facing firewall.
