Question: How does installing software on your PC protect a router (and consequently your game console and the rest of your networked devices) from attack?
Maybe the product I am thinking of, is not the product you guys are describing?
To minimize the effects of attacks, the 1st point of defense should be the 1st point of attack... not the last. The 1st point would be at the ISP routers (which you cannot control, but you can contact them when you are attacked), but then your own router(s). The DOS is not just your game console, it is a disruption of your access to the internet. Although having a good firewall on any device is a good thing (more so, not a bad thing), a firewall on an internal device is redundant if the malignant packets never get there.
Say you're using skype or a torrent program. Both of them need to connect to somewhere outside your computer. When the firewall is put at it's highest alert, then whenever an unknown or even known IP (still can't think of name) tries to connect with your computer or router, it'll alert you with a pop-up, asking your permission if you want to allow this address to access your computer or router. Packets also go through your computer (or so I'm told) and someone who knows alot about this told me that sometimes, in order to fully shut you down, it needs to connect to the items it needs to shutdown in case of ( I forgot what internet thingy he said ) and so if you choose to block and terminate the connection, it won't connect. I also recommend this for AV because of this function and that way you can identify unknown files and find the viruses and block them. It's worked for me in the past.
You can also get a VPN like cyberghost VPN is one I recommend because if they can't obtain your IP, they can't attack you and comodo also alerts you if someone is trying to track you.
Packets destined for 1 device do not go to another (unless you are using a hub, and not a router). If someone bogs down your router, nothing is getting out of your network.
I had to buy a 250 dollar scrambler to hide my IP address so they couldn't pin point my location and boot me, its such a pain in the ass. I hope with the Clan Battles in Ghosts IW does something about this.