If they were to actually manage to take down the root DNS servers, then DNS lookups would fail, so for the average user who doesn't know what an IP address is, let alone what one to use or how to enter it, the internet would be taken down. There are a large number of cavets to this exercise though. Firstly, none of those nameservers are actually servers. The IPs point to dozens and dozens and dozens of machines each (keep in mind all of these are queried for most internet traffic in the world.) Billions upon billons of lookups preformed regularly. To overwhelm something of this magnitude would take a lot of effort. Secondly, there is DNS caching done locally, at the local network level, and the ISP level.ISPs generally only cache for a few hours at most, usually much much less. They would have to have a sustained attack to outlive this caching in order to be effective. Thirdly, if this even comes close to happening, some of the smartest people in the networking world will step forward to fix it (remember Slammer, or the network issues when the middle east cables were cut?)

Possible? Yep. Plausible? It just depends on how much force they are putting behind it.

Not even a little bit, the whole thing was written by someone who has no idea how the internet works. Even if they somehow managed to get all 13 DNS root servers offline at once, most people would never notice since there are several layers of caching between you and the root DNS servers. The vast majority of DNS queries never hit the root servers.