First, depending on how his account got hacked, a router probably won't do diddly to help prevent his WoW account from being hacked again. That said, I do suggest he use a router to increase overall security. It works like this.
When you sign onto the internet, your ISP gives you whats called an IP address. It looks something like this, 123.45.67.89. When you add a router, IT takes the IP address, 123.45.67.89, and assigns your computer a new address, 192.168.0.100. The 192.168.x.x numbers are special in that they are "non routable." Someone from outside your house/home network can't type 192.168.0.100 into their computer and talk to yours. Without a router, they could type in 123.45.67.89 and attempt to access your computer. They could type in 123.45.67.89, but then they are talking to your router, which is harder to gain access to then a windows machine. (assuming ofcourse you changed the login info.)