The article talks about this being a small local area network. No discussion about it being connected to the Internet. This is the best firewall of all - a physical air gap between you and the rest of the universe. In many respects this is the best security. So what do local firewalls on each box achieve? In this context virtually nothing except CPU overhead. The database server shouldn't be exposing anything but the database port anyway. The client need not expose any endpoint at all. Configure it this way and there is little opportunity for compromise.
Now as a way to protect your internal lan from the evils of the Internet a firewall is a great idea on the edge, but again they provide very little protection running on the internal servers. You can't just sprinkle firewalls over your network and assume security. They are a tool to limit a specific kinds of attack; to insulate your internal network from external bad actors. If you have a office and servers put the servers behind their own firewall.