The listed DNS servers will block various Nintendo URLs that the Wii U communicates with. In other words, these servers are built to prevent updates to your Wii U. You need to set two of them, because if one goes down - the other will kick in and work.
Connecting directly to another computer knowing only the MAC address? Ask Question 12. From my understanding, ARP translates an IP address into a MAC address, and then the computer uses the MAC address to establish a direct connection. For example, there are network protocols other than IP that work over ethernet, and the drivers that. The MAC address is intended to assist your network in getting you the packets intended for you rather than your co-worker sitting next to you. For legitimate devices it is directly tied to the hardware and often burned into 'rom' on the network card itself (but sometimes it's not actually read only).
Step 1) Enter Sytem Settings from the system menu.
Step 2) Select 'Internet' for internet settings.
Step 3) Select 'Connect to the Internet'
Step 4) Connect to the internet. If you have already configured an internet connection, Press 'X' to display connections.
Step 5) Select your default connection
Step 6) Select 'Change Settings'
Step 7) Find the DNS section and select it.
Step 8) Select 'Don't Auto-obtain'.
Step 9) Set both of the following to the 'Primary DNS' and 'Secondary DNS'.
Step 10) Hit 'Confirm'
Step 11) Press 'B' to save
Follow this guide by Tgames of GBATemp about blocking auto-updates via a proxy server. This will work, however it requires that a computer always be on.
If your router has the option to block certain URLs from passing through, that's a way better way of keeping your Wii U safe and connected. After setting this up, I don't think you will be able to access the eShop, but you should be able to play games online just fine. (*If you still want eShop access, check out the /r/wiiuhacks wiki). Here are the URLs to block if you can:
Note: Router URL Blocking will block all things Nintendo. This means that if you have any kind of 3DS, it will not be able to preform updates either. Other Wii U consoles connected to that router won't be able to update as well.
As an added precaution, you can also do as the header says: disable automatic software downloads. If you go into internet settings, the option to enable/ disable is below the 'View Mac Address' button. (Thanks /u/KingGhidorah01)